LI  BR  A  FLY 

OF   THE 

UNIVERSITY 

or    ILLINOIS 

3TO 


Return  this  book  on  or  before  the 
Latest  Date  stamped  below. 


University  of  Illinois  Library 


'±  ...J-i 


n--    c;,(: 


in^L 


H^K  maid     y^ 


h^  ^ 


>  ^oW 


"'  f'J        HI      -  •      If)  [- 

^'    O     1  if.'        :O0 


'JUN  0  3  1983 
JULl 


HA 


21983 


^  0  8  2006 


LI61  — H41 


Digitized  by  the  Internet  Archive 

in  2011  with  funding  from 

University  of  Illinois  Urbana-Champaign 


http://www.archive.org/details/predictingschola37odel 


BULLETIN  XO.  37 


BUREAU  OF  EDUCATIONAL  RESEARCH 
COLLEGE  OF  EDUCATION 


PREDICTING  THE  SCHOLASTIC  SUCCESS 
OF  COLLEGE  FRESHMEN 

By 

Charles  W.  Odell 

Assistant  Director,  Bureau  of  Educational  Research 


PRICE  25  CENTS 


PUBLISHED  BY  THE  UNIVERSITY  OF  ILLINOIS,  URBANA 

1927 


TABLE  OF  CONTENTS 

PAGE 

Preface         5 

Chapter  I.     Introduction  and  Statement  of  the  problem       .       7 

'  Chapter  II.     A  brief  Review  of  What  Has  Already  Been 

Done 10 

1  Chapter  III.     The  General  Plan  of  This  Study    ....     20 

Chapter  IV.     The  Simple  Correlations  Between  Freshman 

Marks  and  the  Other  Data  Collected 28 

W  Chapter  V.     The  Multiple  Correlations  Between  Freshman 

Marks  and  the  Other  Data  Collected     ....     34 

I  Chapter  VI.     The  Accuracy  of  Predictions  Based  upon  the 

Obtained  Coefficients  of  Correlations        ....     40 

I  Chapter  VII.     Is  the  Change  from  High  School  to  College 

Greater  than  that  from  Elementary  to  High  School?     48 

Chapter  VIII.     Summary  and  Conclusions 52 


PREFACE 

The  prediction  of  the  scholastic  success  of  college  freshmen  is  com- 
manding the  attention  of  many  persons,  especially  those  who  are  respon- 
sible for  the  administration  of  colleges  and  universities.  It  has  been 
proposed  that  by  making  use  of  a  student's  high-school  record  and  by 
administering  an  intelligence  test  it  would  be  possible  for  an  institution 
to  predict  the  probable  success  of  an  entering  student  in  the  various 
subjects  of  instruction.  It  is,  of  course,  generally  recognized  that  such 
predictions  would  not  be  accurate  in  all  cases.  Some  authorities  contend 
that,  if  sufficient  information  is  secured  and  the  prediction  is  made  in- 
telligently, it  will  be  sufficiently  accurate  to  be  very  helpful  in  guiding 
the  student  when  he  enters  college.  Other  authorities  maintain  that  in 
general  the  prediction  will  be  so  inaccurate  that  it  will  not  be  very 
useful. 

In  this  bulletin  Dr.  Odell  presents  the  results  of  a  very  careful  in- 
quiry into  the  accuracy  of  predictions  that  may  be  made  using  certain 
information.  Although  knowing  the  probable  accuracy  of  the  predic- 
tions that  may  be  made  does  not  determine  the  value  of  such  predic- 
tions, it  should  be  helpful  to  college  administrators  to  know  the  probable 
accuracy  of  the  predictions  they  may  make.  Hence,  it  is  believed  that 
Dr.  Odell's  study  constitutes  a  significant  contribution  In  the  field  of 
college  administration. 

Walter  S.  ]\  Ion  roe,  Director 
May  4,  1927 


[5] 


PREDICTING  THE  SCHOLASTIC  SUCCESS 

OF  COLLEGE  FRESHMEN 

CHAPTER  I 

INTRODUCTION  AND  STATEMENT  OF  THE  PROBLEM 

The  recent  increase  in  college  enrollment  and  two  resulting 
problems.  In  a  previous  publication^  the  present  writer  has  called  at- 
tention to  the  fact  that  one  of  the  most  notable  and  significant  recent 
educational  tendencies  in  this  country  has  been  the  marked  increase  in 
school  enrollment,  especially  on  the  secondary  and  higher  levels.  Such 
a  tendency  has,  it  is  true,  existed  from  the  beginning  of  our  educational 
system,  but,  since  sometime  near  the  end  of  the  Nineteenth  Century  and 
even  more  since  the  close  of  the  World  War,  it  has  been  greatly  accentu- 
ated. This  may  be  seen  from  the  last  Statistical  Summary  of  Education- 
issued  by  the  United  States  Bureau  of  Education,  which  shows  that  at 
present  between  three-fourths  and  one  per  cent  of  our  whole  population 
is  enrolled  in  college,  whereas  in  1890  only  about  one-fourth  of  one  per 
cent  was  so  enrolled.  The  figures  given  also  show  that  the  last  five-year 
period  has  exhibited  a  much  greater  increase  than  any  other  of  similar 
length. 

Concurrent  with  the  tendency  just  stated  have  been  a  considerable 
decline  in  the  purchasing  power  of  the  dollar  and  a  general  demand  that 
the  scope  of  education  be  enlarged.  The  united  effect  of  these  three 
factors  has  been  such  that  it  is  practically  impossible  to  secure  the 
amounts  of  money  necessary  to  provide  what  are  considered  adequate 
educational  facilities  for  all  those  who  wish  to  enjoy  them.  The  diffi- 
culty of  doing  so  appears  to  be  greater  in  the  field  of  higher  education 
than  in  any  other. 

One  outstanding  question,  which  has  arisen  in  connection  with  the 
crucial  situation  just  described,  is  that  of  whether  or  not  institutions  of 
higher  education  shall  open  their  doors  to  practically  all  those  who 
have  completed  a  secondary  course  and  wish  to  enter.  The  general 
tendency  has  been  for  state  supported  institutions  to  approximate  doing 


'Odell,  C.  W.  "Are  college  students  a  select  group. '"■"  University  of  Illinois  Bulle- 
tin, Vol.  24,  Xo.  36,  Bureau  of  Educational  Research  Bulletin  Xo.  34.  Urbana:  Uni- 
versity of  Illinois,  1927.   45  p. 

^Phillips,  Frank  M.  '"Statistical  summary  of  education  1923-24."  U.  S.  Bureau 
of  Education  Bulletin,  1926,  Xo.  19.  Washington,  1926.   7  p. 

[7] 


so,  whereas  those  deriving  their  support  from  other  sources  exercise 
varying  degrees  of  selection  among  the  appHcants  for  admission.  These 
policies  are  rarely  based  upon  any  thoroughgoing  study  of  the  problem 
and  never  upon  conclusive  evidence  as  to  the  best  practice,  so  that 
■what  should  be  done  may  be  considered  still  an  open  question.  The  data 
available^  appear  to  warrant  the  statement  that  at  present  the  group  of 
those  who  actually  enter  college  represents  a  marked  selection  of  all 
high-school  graduates,  but  that  it  still  contains  many  individuals  who 
apparently  cannot  carry  the  usual  type  of  college  work  successfully.  On 
the  Avhole.  therefore,  it  seems  desirable,  perhaps  even  necessary,  that  if 
colleges*  are  to  continue  to  maintain  their  present  scholastic  standards, 
some  degree  of  selection  among  applicants  for  admission  should  be  exer- 
cised. Such  an  assumption  naturally  raises  the  question  as  to  what  is 
the  most  desirable  basis  of  making  this  selection.  In  other  words,  do 
any  of  the  data  which  are  fairly  readily  obtainable  concerning  high- 
school  graduates  provide  a  satisfactory,  or  even  a  helpful,  basis  of  fore- 
telling scholastic  success  in  colleger  If  so,  which  of  these  data  are  most 
valuable  for  this  purpose  and  how  much  confidence  should  be  placed 
in  their  use.' 

A  second  question  arising,  in  part  at  least,  from  the  same  cause 
and  one  which  has  attracted  much  attention  recently  is  that  of  providing 
for  college  students  of  different  aptitudes  and  abilities.  This  question 
really  divides  itself  into  two  parts.  In  the  first  place,  if  the  amount  of 
selection  at  college  entrance  is  not  very  great  it  will  undoubtedly  result 
that  many  of  those  who  are  allowed  to  enter  can,  or  at  least  will,  not 
do  satisfactory  work  in  certain  subjects,  whereas  in  others  they  will 
do  passing  or  even  superior  work.  The  college  is  therefore  confronted 
with  the  need  for  providing  educational  guidance  for  such  students. 
This  requires,  if  possible,  the  determination  of  the  subjects  or  courses  in 
which  the  students  will  succeed  and  those  in  which  they  will  fail.  Even 
if  entrance  requirements  are  decidedly  severe  and  many  of  those  seek- 
ing admission  are  barred,  educational  guidance  of  the  sort  just  men- 
tioned is  still  desirable  though  the  necessity  for  it  is  not  so  acute.  In 
the  second  place,  there  has  recently  been  considerable  interest  in  the 
matter  of  offering  different  types  or  levels  of  instruction  within  single 
subjects  and  otherwise  varying  the  educational  opportunities  given  stu- 
dents of  different  abilities.  It  is  true  that  this  problem  has  received 
much  more  attention  in  elementary  and  high  schools  than  in  colleges, 


^Odell,  op.  cit.,  p.  26-29. 

*The  term  "college"  will  be  used  frequently  as  a  general  term  including  all  types 
of  institutions  of  higher  learning. 

[8] 


but  an  increasing  number  of  the  latter  are  giving  it  serious  consideration. 
In  this  case  also,  the  less  selection  there  is  among  applicants  for  admis- 
sion to  college  the  greater  is  the  need  for  attention  after  admission  be- 
cause the  group  admitted  is  more  heterogeneous.  Even  if  a  relatively 
high  degree  of  selection  is  exercised  among  those  who  seek  to  enter  col- 
lege, however,  those  who  gain  admission  and  who  enroll  for  any  partic- 
ular subject  practically  never  constitute  a  truly  homogeneous  group. 
Therefore,  there  is  need  to  determine  the  validity  of  various  bases 
which  may  be  employed  for  classifying  students  in  advance  according  to 
the  different  amounts  and  kinds  of  subject  matter,  types  of  instruction, 
and  so  forth,  which  seem  best  suited  to  them. 

The  purpose  of  this  bulletin.  It  is  the  purpose  of  this  bulletin  to 
present  a  study  and  evaluation  of  some  of  the  more  readily  available 
items  of  information  which  may  be,  and  in  many  cases  are,  used  to  pre- 
dict the  probable  scholastic  success  of  college  students.  After  reviewing 
briefly  a  number  of  studies  illustrative  of  what  has  already  been  done  in 
the  field,  the  writer  will  give  an  account  of  one^  along  this  same  line 
which  he  has  been  carrying  on.  This  investigation  differs  from  most  of 
the  others  in  the  same  field  in  that  the  attempt  has  been  made  not 
merely  to  determine  the  accuracy  of  prediction  of  college  success  in 
general,  but  also  for  each  subject  carried  by  any  considerable  number 
of  the  individuals  included.  It  is  limited  by  the  fact  that  the  college 
data  upon  which  it  is  based  include  only  records  for  the  freshman  year. 
Its  purpose  may,  therefore,  be  stated  as  being  to  show  how  accurately 
the  marks  of  college  freshmen  in  their  various  subjects  can  be  pre- 
dicted when  their  ages,  scores  upon  an  intelligence  test,  and  complete 
high-school  records  are  available.  The  problem  will  be  attacked  pri- 
marily by  the  methods  of  simple  and  multiple  correlation  and  the  ac- 
curacy of  predictions  based  on  the  best  multiple  regression  equations 
obtainable  will  be  shown. 


^The  first  part  of  this  study,  which  inchided  only  the  data  obtained  while  the  in- 
dividuals embraced  were  still  in  high  school,  has  been  presented  in  the  following  bul- 
letin: 

Odell,  C.  \V.  "'Conservation  of  intelligence  in  Illinois  high  schools."  University 
of  Illinois  Bulletin,  \'ol.  22,  No.  25,  Bureau  of  Educational  Research  Bulletin  No.  22. 
Urbana:  University  of  Illinois,  1925.   55  p. 

A  second  portion  which  deals  with  the  question  of  how  great  a  selection  occurs 
among  college  entrants  as  compared  with  high-school  graduates  has  been  dealt  with  in 
the  following  publication: 

Odell,  C.  W.  "Are  college  students  a  select  group?"  University  of  Illinois  Bulle- 
tin, Vol.  24,  No.  36,  Bureau  of  Educational  Research  Bulletin  No.  34.  Urbana:  Uni- 
versity of  Illinois,  1927.   45  pp. 

The  present  bulletin  is  the  third  in  the  series. 

[9] 


CHAPTER  II 

A  BRIEF  REVIEW  OF  WHAT  HAS  ALREADY. 
BEEN  DONE 

The  extent  to  which  intelligence  tests  have  been  used  in  institu- 
tions of  higher  learning.  Since  most  of  the  recent  studies  dealing  with 
the  prediction  of  scholastic  success  in  college  have  employed  intelligence 
test  scores  as  the  chief  criterion,  it  seems  in  place  to  mention  several 
studies  which  show  something  of  the  extent  to  which  intelligence  tests 
have  been  employed  in  college,  both  for  this  and  other  purposes.  Here 
and  later  no  attempt  will  be  made  to  refer  to  all  of  the  investigations 
which  have  been  reported,  but  only  a  few  of  the  most  significant  or  typ- 
ical ones  will  be  mentioned  in  each  case.  Bridges/  early  in  1922,  re- 
ceived answers  from  42  of  70  institutions  to  which  he  had  sent  inquir- 
ies and  found  that  although  3  1  of  the  42  had  made  some  use  of  group 
Intelligence  tests  only  a  few  had  done  so  in  connection  with  determining 
admission.  Apparently,  in  many  cases,  the  tests  were  administered 
with  no  very  definite  purpose  in  mind.  A  year  and  a  half  later  Laird 
and  Andrews'-  reported  that  26  out  of  64  institutions  made  some  use  of 
tests  as  part  of  the  routine  process  of  determining  the  admission  of  ap- 
plicants and  that  others  used  tests  for  such  purposes  as  sectioning 
classes,  determining  the  amount  of  work  to  be  carried,  giving  vocational 
and  educational  guidance,  deciding  upon  the  elimination  of  students,  and 
dealing  with  disciplinary  cases.  Probably  the  most  detailed  report  of 
the  use  of  intelligence  tests  in  colleges  is  that  by  MacPhail,^  which  ap- 
peared some  three  years  ago.  In  this  he  summarized  briefly  almost 
every  article  dealing  with  this  topic  and  showed  that  in  many  institu- 
tions intelligence  tests  played  a  definite  part  in  the  admission  of  appli- 
cants as  well  as  in  other  questions  of  policy.  A  more  recent  study  by 
Toops*  reported  that  66  out  of  110  institutions  answering  a  question- 
naire employed  intelligence  tests  during  the  year  1923-24.   Xone  of  these 


'Bridges,  J.  W.  "The  value  of  intelligence  tests  in  universities,"  School  and  So- 
ciety, 15:295-303,  March  18,  1922. 

'Laird,  D.  A.,  and  Andrews,  A.  "The  status  of  mental  testing  in  colleges  and 
universities  in  the  United  States,"  School  and  Society,  18:594-600,  November  17,  1923. 

'M.a.cPh.4il,  a.  H.  The  Intelligence  of  College  Students.  Baltimore:  \\'ar\vick 
and  York,"  1924.    176  p. 

*Toops,  H.  A.  "The  status  of  university  intelligence  tests  in  1923-24,"  Journal  of 
Educational  Psychology,   17:23-36,   110-24,  January,  February,   1926. 

[10] 


based  admission  entirely  upon  test  results,  but  19  used  them  as  a  partial 
basis.  Forty-nine  took  them  into  account  in  determining  dismissal  for 
low  scholarship,  34  in  determining  probation,  36  used  the  results  in  de- 
termining the  amount  of  work  students  should  carry.  25  in  selecting  and 
encouraging  bright  students  to  take  graduate  work,  42  in  motivating  the 
work  of  bright  students,  and  various  numbers  in  selecting  assistants, 
appointing  scholars  and  fellows,  and  so  on. 

From  the  studies  referred  to  above  it  will  be  seen  that  intelligence 
testing  is  apparently  well  established  in  many  institutions  of  higher 
learning  and  that  the  results  receive  large  use  in  a  number  of  matters 
having  to  do  with  guidance,  instruction,  and  other  direction  of  students, 
as  well  as  to  a  somewhat  lesser  degree  with  their  admission.  So  far  as 
the  WM'iter  knows,  no  institution  has  yet  based  admission  upon  intelli- 
gence test  scores  alone,  though  for  certain  classes  of  applicants  a  few 
colleges  make  them  the  chief  criterion."' 

Summary  studies  of  the  relationship  of  intelligence  test  scores 
and  other  criteria  to  college  marks.  Several  of  the  studies  mentioned 
and  a  number  of  others  present  data  showing  the  degree  of  relationship 
found  between  college  marks  and  intelligence  test  scores,  high-school 
marks,  and  other  items  of  information.  Before  considering  a  few  re- 
ported investigations  in  greater  detail  it  seems  well  to  give  a  brief  pic- 
ture of  general  tendencies.  Terman,''  reporting  on  25  colleges,  found  co- 
efficients of  correlation"  running  from  .29  to  .83  between  test  scores  and 
college  marks,  whereas  those  between  the  latter  and  high-school  marks 
ranged  from  .38  to  .74,  and  those  between  them  and  college  entrance 
examination  results  from  .25  to  .62.  Incidentally,  he  states  that  the 
Thorndike  Intelligence  Examination  is  probably  the  best  of  those  avail- 
able for  the  purpose  of  predicting  scholastic  success  in  college.  Roberts^ 
reports  similar  ones  of  .31  to  .60.  also  coefficients  between  college  and 
I  high-school  marks  of  .53  to  .69  and  between  the  former  and  college  en- 
trance examinations  of  .25  to  .62.  He  makes  this  statement,  "'Combining 
intelligence  scores  with  all  other  good  measures,  the  exceedingly  high 
correlations   of   .75    to   .80   are   obtained  between   these   measures    and 


"This  refers  chiefly  to  the  admission  or  rejection  of  applicants  who  have  not  com- 
pleted the  required  secondary  school  work  and  who  are  also  above  the  usual  age. 

*Terman,  L.  M.  "Intelligence  tests  in  colleges  and  universities,"  School  and  So- 
ciety. 13:481-94.  April  23,  1921. 

'The  meaning  and  interpretation  of  coefficients  of  correlation  of  \'arious  sizes  is 
discussed  in  Chapter  M. 

^Roberts,  A.  C.  "Objective  measures  of  intelligence  in  relation  to  high-school  and 
college  administration,"  Educational  Administration  and  Supervision.  8:530-40,  Decem- 
ber, 1922. 

[11] 


scliool  marks.''  He  also  writes,  ''The  intelligence  scores  have  shown 
themselves  our  surest  guide  in  detecting  the  very  highest  and  the  very- 
lowest  of  intellectual  ability."  MacPhail^  lists  about  60  correlations  be- 
tween test  scores  and  college  marks,  ranging  from  .13  to  .71. 

The  use  of  intelligence  tests  at  Brown  University.  Due  to  the 
work  of  Colvin,  assisted  b}'  MacPhail  and  others.  Brown  University  has 
for  about  ten  years  been  among  those  institutions  making  the  most  ex- 
tensive and  careful  use  of  intelligence  tests  in  connection  with  the  ad- 
mission of  students  and  also,  though  perhaps  to  a  lesser  degree,  in  con- 
nection with  their  guidance  and  direction  after  entrance.  Not  only  have 
intelligence  tests  played  a  prominent  part  in  determining  the  admission 
of  freshmen  at  Brown  University,  but  also  a  number  of  articles  have  ap- 
peared describing  their  use  for  this  purpose.  Therefore  it  seems  fitting 
to  select  this  institution  as  the  example  which  will  be  described  in  more 
detail  than  any  other  as  an  illustration  of  what  Is  being  done. 

The  work  along  this  line  began  during  the  time  of  the  World  War 
and  by  1919  Colvin^'^  reported  on  the  first  two  or  three  years'  use  of 
tests.  At  this  time  he  stated  that  different  intelligence  tests  correlated 
from  about  .40  to  .60  with  freshman  marks,  and  that  of  the  students 
who  did  unsatisfactory  or  unusually  good  work  about  two-thirds  were 
indicated  by  the  test  scores.  On  the  whole  the  results  were  considered 
sufficiently  satisfactory  to  warrant  continuing  the  use  of  tests.  A  year 
later  another  article^^  by  the  same  writer  gives  about  the  same  correla- 
tions as  before,  those  for  the  Brown  University  Psychological  Examina- 
tion and  the  Thorndike  Intelligence  Examination  being  a  number  of 
points  higher  than  those  for  Army  Alpha  and  also  being  on  the  whole 
higher  than  the  corresponding  correlations  for  high-school  marks  or 
teachers'  estimates.  The  test  results  appeared  to  pick  out  the  superior 
and  inferior  students  with  more  accuracy  than  the  average  ones.  When 
the  Brown  and  Thorndike  scores  were  averaged  90  per  cent  of  the  low- 
est tenth  were  found  to  have  failed  in  one  or  more  subjects. 

In  1922  Colvin  and  MacPhaiF-  replied  to  some  unfavorable  criti- 
cisms of  the  use  of  intelligence  tests  in  college  and  gave  further  data 
concerning  their  use  at  Brown  University.  Most  of  these  merely  sub- 
stantiate previous  statements,  though  in  some  cases  they  are  presented 


'MacPhail,  op.  cit.,  p.  29. 

'"Colvin,  S.  S.  "Psvchological  tests  at  Brown  University,"  School  and  Society, 
10:27-30,  July  5,  1919. 

"Colvin,  S.  S.  "Validity  of  psychological  tests  for  college  entrance,"  Educational 
Review,  60:7-17,  June,  1920.  ' 

"Colvin,  S.  S..  and  MacPhail,  A.  H.  '"The  value  of  psychological  tests  at  Brown 
University,"  School  and  Society,  16:113-22,  July  29,  1922. 

[12] 


in  a  different  form.  The  writers  state,  for  example,  that  low  test  scores 
furnish  a  more  reliable  prediction  that  college  work  in  general  will  be 
poor  than  do  low  marks  made  during  the  first  semester  but  that  a  com- 
bination of  the  two  is  better  than  either  one  alone.  Of  college  honors  80 
per  cent  went  to  those  earning  high  test  scores,  19  per  cent  to  those  with 
medium  scores,  and  only  1  per  cent  to  those  with  low  scores. 

A'lore  recently  Burwell  and  MacPhaiP'  have  written  upon  the  same 
topic.  They  report  that  the  procedure  has  been  changed  somewhat  by 
giving  the  Brown  test  to  all  freshmen  and  the  Thorndike  test  only  to  the 
lowest  fifth,  in  place  of  giving  both  to  all  freshmen  as  had  been  done  for 
several  years.  Among  the  statements  made  are  that  "new  students  who 
will  probably  fail  in  two  or  more  subjects  in  either  semester  during  their 
first  year  in  college  are  far  more  likely,  roughly  speaking  ten  to  twenty 
times  more  likely,  to  be  found  among  those  who  make  low  psychological 
scores  than  among  those  with  high  ratings;"  that  "a  freshman  whose 
psychological  score  places  him  in  the  lowest  decile  has  only  two  chances 
out  of  five  of  remaining  more  than  one  year  in  college  and  only  one 
chance  out  of  five  of  graduating;"  and,  finally,  that  "the  majority  of 
honor  men  are  to  be  sought  among  those  scoring  in  the  best  psychologi- 
cal third;  most  of  the  remainder  may  be  expected  to  come  from  the 
middle  third;  and  a  very  few  (about  one  out  of  twenty)  from  the  lowest 
third."  Forty-six  has  been  set  as  a  critical  score  on  the  Brown  Univer- 
sity test  above  which  a  student  must  rate  to  indicate  that  he  will  prob- 
ably receive  no  grades  below  "C"  during  the  first  semester. 

It  appears  that  those  who  have  been  using  the  tests  at  Brown  are 
very  firmly  convinced  of  their  value.  However,  they  recognize  and 
point  out  certain  limitations  and  indicate  that  it  is  highly  desirable  to 
have  other  data  to  supplement  the  test  results,  but  apparently  regard 
them  as  the  one  most  important  criterion  for  predicting  scholastic  suc- 
cess in  college. 

The  use  of  tests  at  Columbia  University.  Columbia  University, 
also,  has  made  rather  extensive  use  of  intelligence  tests  in  connection 
with  admitting  students.  Accounts  of  the  work  have  been  given  by 
^^  ood,^'*  Thorndike. '■'  and  others.  The  experiments  there  appear  to  have 
begun  in  1919.  At  that  time  faculty  action  was  taken  providing  two  pos- 
sible methods  of  entrance,  one  of  which  was  the  old  method  based  upon 

"Burwell,  W.  R..  and  MacPhail,  A.  H.  '"Some  practical  results  of  psychological 
testing  at  Brown  University,"  School  and  Society,  22:48-56.  July  11,  1925. 

"Wood,  B.  D.  Measurement  in  Higher  Education.  New  York:  World  Book  Com- 
pany, 1923,  Chapters  U-V. 

"Thorxdike,  E.  L.  '"On  the  new  plan  of  admitting  students  at  Columbia  Univer- 
sity," Journal  of  Educational  Research,  4:95-101,  September.  1921. 

[13] 


entrance  examinations  in  high-school  subjects,  previous  school  records, 
health  records,  and  estimates  of  character  and  personality.  The  second 
method  substituted  intelligence  tests  for  the  subject-matter  examinations 
included  in  the  first.  For  purposes  of  record  all  those  desiring  to  enter 
by  the  first  plan  as  well  as  those  entering  by  the  second  are  given  the 
Thorndike  Intelligence  Examination.  Many  different  sets  of  figures  are 
given  to  indicate  the  validity  of  this  test  as  used  at  Columbia  for  fore- 
casting success  in  college  work.  The  correlations  between  test  scores 
and  college  marks  average  around  .65  and  are  distinctly  higher  than 
those  of  the  latter  with  college  entrance  examinations,  New  York  Re- 
gents' examinations,  and  still  more  so  than  those  with  secondary-school 
marks.  The  correlations  obtained  for  the  test  results  are  probably  in- 
creased somewhat  because  no  applicant  for  admission  is  allowed  to  take 
the  test  unless  the  data  concerning  him  on  the  other  three  points  men- 
tioned are  satisfactory.  The  same  is,  however,  true  of  those  admitted 
wath  examinations  covering  high-school  subjects  as  one  of  the  criteria 
and  doubtless  raises  the  correlations  there  also.  In  conclusion  it  may 
be  said  that  the  use  of  intelligence  tests,  as  one  of  the  bases  for  de- 
termining admission  to  Columbia  University,  has  become  an  integral 
part  of  the  procedure  and  is  no  longer  considered  an  experiment. 

The  use  of  intelligence  tests  at  the  University  of  Minnesota.  The 
reports^'''  from  this  institution  are  not  as  favorable  to  intelligence  tests 
as  those  from  Brown  and  Columbia  Universities.  It  appears  that  high- 
school  marks,  the  kind  of  work  carried  in  high  school,  and  marks  on 
three  themes  at  the  beginning  of  the  freshman  year  at  the  University 
were  all  more  reliable  in  indicating  students  whose  university  work  was 
poor  than  were  the  scores  made  on  a  mental  test.  \\  hen  the  latter  were 
combined  with  the  former,  a  correlation  of  about  .70  was  obtained.  It 
is  pointed  out  that  in  most  cases  of  marked  discrepancy  between  the 
work  actually  done  and  the  predictions  made  from  the  combined  cri- 
teria explanations  can  be  found  when  the  individual  cases  are  studied. 
What  has  been  accomplished  at  the  University  of  Minnesota  may  be 
summarized  as  follows:  a  threshold  has  been  fixed  such  that  only  1 
per  cent  of  those  falling  below  it  will  prove  successful  in  college  work; 
the  procedure  can  be  explained  to  students  and  all  others  interested; 
students  of  unusual  ability  can  be  located;  a  beginning  of  vocational  se- 

"JoHNSTON,  J.  B.  ''Predicting  success  in  college  at  the  time  of  entrance,"  School 
and  Society,  23:82-88,  January  16,  1926. 

JoHN-STOx,  J.  B.  ""Predicting  success  or  failure  in  college  at  the  time  of  en- 
trance." School  and  Society,  19:772-76,  June  28,  1924;  20:27-32,  July  5,  1924. 

Johnston,  J.  B.  '"Tests  for  ability  before  college  entrance,"  School  and  Society, 
15:345-53,  April  1,  1922. 

[14] 


lection  has  been  made;  promising  students  not  in  college  can  be  selected 
and  encouraged  to  attend;  college  failures  can  be  treated  much  more 
adequately;  students  who  need  special  advice  can  be  selected  and  given 
this  advice;  and  finally  each  student  guided  "so  far  as  possible  into  that 
line  of  eff^ort  in  which  his  native  ability  will  find  Its  most  complete  ex- 
pression." 

The  use  of  intelligence  tests  at  other  institutions.  In  view  of  the 
fact  that  there  is  great  similarity  between  the  results  reported  from 
most  of  the  institutions  which  have  employed  intelligence  test  scores  as 
one  of  the  criteria  for  determining  admission,  it  seems  not  worth  while 
to  refer  to  reports  from  more  than  a  few  difi"erent  institutions.  Those 
which  are  mentioned  in  this  section  were  chosen  partly  more  or  less  at 
random  and  partly  because  the  results  obtained  were  in  some  way 
different  from  the  general  trend. 

The  results  reported  from  the  University  of  Pittsburgh^"  are  dis- 
tinctly lower  than  those  given  previously.  In  this  case  college  marks 
correlated  only  .41  with  Army  Alpha  Scores,  as  compared  with  .32  with 
first  semester  marks.  These  correlations  were  undoubtedly  lowered 
somewhat  by  the  fact  that  the  individuals  included  in  the  study  were 
more  highly  selected  than  an  ordinary  freshman  class,  and  also  by  the 
fact  that  the  Army  Alpha  Test  seems,  on  the  whole,  not  to  predict 
scholarship  as  well  as  do  the  Thorndike,  Brown,  and  several  others. 
Differing  much  from  this  is  an  unusually  high  correlation  reported  from 
the  State  Normal  School  at  Indiana,  Pennsylvania.^*  The  National  and 
Illinois  Intelligence  Tests  were  used  and  the  scores  correlated  above  .70 
with  educational  psychology  mark. 

May,  at  Syracuse  University,'-'  secured  information  as  to  the  num- 
ber of  hours  spent  in  study  and  found  that  combining  this  with  intelli- 
gence test  score  gave  a  multiple  correlation  of  .83,  whereas  test  score  and 
high-school  mark  gave  only  .64  with  honor  points  in  college.  He  also 
found  that  when  the  amount  of  study  was  held  constant  the  correlation 
between  test  score  and  honor  points  was  .81.  A  study  at  the  University 
of  Washington'-'^  corroborates  this,  although  it  does  not  present  its  re- 
sults in  just  the  same  way.     Wilson,  who  reports  it,  concludes  that  the 


"Ernst,  J.  L.  "Psychological  tests  vs.  the  first  semester's  grades  as  a  means  of 
academic  prediction,"  School  and  Society,  18:419-20,  October  6,  1923. 

"Rich,  S.  G..  and  Skinner,  C.  E.  ''Intelligence  among  normal  school  students," 
Educational  Administration  and  Supervision,  11:639-44,  December,  1925. 

"May,  M.  a.  '"Predicting  academic  success,"  Journal  of  Educational  Psychology. 
14:429-40,  October.  1923. 

^"Wilson,  W.  R.  '"Mental  tests  and  college  teaching."  School  and  Society, 
15:629-35,  June  10,  1922. 

[15] 


TABLE  I.     COEFFICIENTS  OF  CORRELATION  BETWEEN  THORNDIKE 
TEST  SCORE  AND  FIRST  SEMESTER  COLLEGE  MARKS 

Biology 51     i  History 46 

Chemistry 43        Human  Progress 69 

English   36     i  Mathematics 52 

French 42        Physics 50 

German 50        Public  Speaking 46 

Graphics 35        Spanish 57 


failure  of  intelligence  tests  and  college  marks  to  correspond  more  closely 
is  largely  accounted  for  by  the  differences  in  the  amounts  of  time  spent 
in  study,  especially  by  the  fact  that,  on  the  whole,  bright  students  study 
less  than  do  dull  ones. 

Studies  showing  correlation  in  particular  subjects  with  intelli- 
gence test  scores  and  other  data.  Most  of  the  many  studies  made  have 
correlated  the  various  criterion  measures  with  college  averages,  only  a 
few  dealing  with  marks  in  particular  college  subjects.  Of  the  few,  two 
which  correlated  test  scores  with  college  marks  and  one  which  used 
high-school  marks  instead  of  test  scores  will  be  mentioned.  One-^  of 
the  first  two  was  made  at  the  University  of  Pittsburgh  and  yielded  the 
average  coefficients  of  correlation  between  score  on  the  Thorndike  test 
and  freshman  college  marks  for  the  first  semester  shown  in  Table  I.  The 
correlation  of  the  test  result  with  the  general  freshman  average  for  the 
first  semester  was  .51.  Root,  who  reports  the  study,  concludes  that  test 
results  are  decidedly  valuable  for  predicting  academic  success,  but  that 
they  are  only  one  of  the  needed  items  of  information.  He  points  out  that 
if  the  criterion  for  admission  to  the  university  were  taken  as  being  the 
lower  limit  of  the  middle  group  upon  the  tests,  all  applicants  scoring 
above  that  point  being  admitted  and  all  below  rejected,  about  one-third 
of  the  students  would  be  excluded  or  admitted  improperly,  that  is,  ex- 
cluded when  they  could  do  satisfactory  work  or  admitted  when  they 
could  not. 

The  other--  of  the  two  studies  does  not  give  tables  of  the  exact 
coefficients  of  correlation,  but  summarizes  the  results  found  from  corre- 
lating Otis  test  score  with  college  marks  as  follows:  'Tn  all  cases  the 
correlations  are  positive.  In  all  cases  on  the  average  the  pupils  who 
stand  high  in  the  test  stand  high  in  scholarship;  those  who  stand  low 
on  the  test  stand  low  in  scholarship,  and  those  who  stand  in  the  middle 


"Root,  \\'.  T.  "The  freshman:  Thorndike  college  entrance  tests,  first  semester 
grades,  Binet  tests,"  Journal  of  Applied  Psychology,  7:77-92,  March,  1923. 

'"JoRDAX,  A.  M.  "Student  mortality.'"  School  and  Society,  22:821-24,  December 
26.  1925. 

[16] 


TABLE   II.     COEFFICIENTS  OF   CORRELATION   BETWEEN   HIGH- 
SCHOOL  AND  COLLEGE  MARKS  IN 
CERTAIN  SUBJECTS 


High 

-School  Subjects 

College  Subjects 

Eng. 

Chem. 

Alg. 

Geom. 

Lat. 

Elem. 
French. 

Adv. 
French 

English 

Chemistry 

.28 
.21 
.22 
.28 
.40 
.39 
.19 

.20 
.19 

.34 
.31 

.26 
.18 

.25 

.18 
.21 
.41 

.38 
.43 
.26 
.31 

.19 
.23 
.41 
.34 
.14 
.03 
.28 

.23 
.23 
.26 
.30 
.14 
.32 
.39 

.25 
.28 
.41 
.38 

^41 

.37 

.31 

.26 

Algebra 

Analytic  Geom 

Elem.  French 

Adv.  French 

German 

.33 
.40 

^35 
.43 

on  the  test  are  in  the  middle  in  scholarship.  But  in  some  cases  the  re- 
lationship is  quite  low,  while  in  other  cases  it  is  moderately  high.  In 
no  case  is  there  a  high  coefficient  of  correlation  between  the  test  and  the 
marks  in  any  subject.  With  German  during  the  first  year  the  relation- 
ship is  quite  respectable,  but,  not  even  here,  high  enough  for  prognosis. 
The  coefficients  are  quite  substantial  (from  .45  to  .61),  then,  between 
the  Otis  test  and  the  marks  in  German,  English,  history,  geology,  and 
French  for  the  first  year;  present  but  low  (.32  to  .39)  in  the  case  of 
mathematics,  chemistry,  Spanish,  economics,  engineering,  and  Latin. 
During  the  second  year  the  coefficients  are  substantial  in  English  and 
Spanish;  present  but  low  in  French,  history,  economics,  engineering,  and 
German;  and  negligible  in  mathematics,  chemistry,  geology,  Latin,  and 
zoology.  However,  the  coefficients  of  correlation  during  the  second  year 
are  necessarily  lower  because  of  the  contraction  of  the  range  of  scores 
(the  lowest  have  largely  disappeared).  The  correlations  with  average 
and  total  grades  are  marked."  Jordan  also  states  the  correlations  ob- 
tained between  high-school  and  college  marks.  These  varied  from  .37 
to  .59  and  on  the  average  were  quite  similar  to  the  coefficients  between 
college  marks  and  test  score.  The  closest  relationships  appeared  to  be 
in  economics,  Spanish,  and  French.  Using  multiple  correlation  with 
combined  test  score  and  high-school  average  mark  he  obtained  a  coeffi- 
cient of  .58  with  the  university  average  for  two  years.  The  conclusion 
from  his  study  is,  therefore,  that  there  is  little  difference  in  prognostic 
power  betwen  the  score  on  the  Otis  Group  Intelligence  Scale,  Advanced 
Examination,  and  the  high-school  mark,  although  the  correlations  of 
the  former  with  college  marks  are  lower  than  those  Root  found  with 
the  Thorndike  score.  This  latter  fact  is  undoubtedly  due,  at  least  in 
part,  to  the  fact   that  the  Thorndike  test  is  considerably  longer  than  that 


[17] 


of  Otis  and  so  yields  a  more  satisfactory  measure  for  the  purpose 
here  discussed. 

The  third  study  referred  to'-^  was  conducted  at  the  University  of 
Alaine  and  dealt  with  the  correlation  of  high-school  and  college  marks  in 
particular  subjects.  The  correlations  found  are  given  in  Table  II. 
These  coefficients  seem  to  warrant  the  conclusion  that  correlations  be- 
tween high-school  marks  and  college  freshman  marks  in  single  subjects 
above  .40  are  rare  and  that  the  central  tendency  of  such  correlations  is 
not  far  from  .30.  This,  however,  is  not  supported  by  the  results  ob- 
tained by  Jordan,  whose  corresponding  coefficients  averaged  about  .20 
higher. 

The  other  studies  of  this  sort  available  tend  to  yield  correlations  of 
about  .40  to  .50  or  .55  between  test  scores  and  marks  in  single  college 
subjects  and  about  the  same  between  high-school  and  college  marks. 
Most  of  them  are  based  on  smaller  numbers  of  cases  covering  only  a 
few  subjects  and  are  hardly  worth  mentioning  separately. 

Summary.  The  work  which  has  been  done  up  to  date  in  attempt- 
ing to  predict  the  scholastic  success  of  college  students  by  means  of 
intelligence  test  scores  and  other  criteria  may  be  briefly  summarized  in 
the  following  statements.  In  a  considerable  number  of  institutions  of 
higher  learning,  including  several  of  the  largest  ones  in  this  country, 
the  use  of  intelligence  test  scores  as  one  of  the  criteria  for  admission 
has  passed  the  experimental  stage  and  is  now  a  settled  policy.  In  many 
other  institutions  much  use  has  been  made  of  intelligence  tests,  but  it 
has  had  little  or  no  connection  with  the  admission  of  students.  Although 
the  correlations  reported  vary  from  near  zero  up  to  .70  or  above,  a 
range  of  .40  to  .50,  or  perhaps  somewhat  higher,  may  usually  be  ex- 
pected between  score  on  an  intelligence  test  and  freshmen  mark.  These 
correlations  are  about  the  same  as  those  of  high-school  with  freshman 
marks  and  both  slightly  higher  than  those  given  by  entrance  examina- 
tions covering  high-school  subjects.  The  true  relationship  in  the  latter 
case  is,  however,  somewhat  closer  than  indicated  by  the  obtained  co- 
efficients of  correlation,  because  applicants  for  admission  making  low 
marks  are  generally  rejected  and  thus  the  range  decreased  and  the  ap- 
parent correlation  lowered.  If  one  of  the  best  tests  is  employed  the 
correlations  with  freshman  mark  will  probably  be  higher  than  will  those 
of  the  high-school  average.  A  combination  of  test  score  and  high- 
school  mark  may  be  expected  to  yield  correlations  of  about  .60  or  higher. 


^^GovvEX,  J.  W'.,  and  Gooch,  M.  "The  mental  attainments  of  college  students  in 
relation  to  pre\ious  training,"  Journal  of  Educational  Psvchologv,  16:547-68.  Xovember. 
1925. 

[18] 


If  it  is  possible  to  include  an  adequate  measure  of  study  habits  also  the 
coefficients  will  probably  rise  to  near  .80.  Comparatively  little  has  been 
done  in  attempting  to  predict  scholastic  success  in  single  college  subjects, 
but  apparently  the  correlations  found  for  single  subjects  are  on  the 
whole  not  much,  if  any,  below  those  found  for  the  general  freshman 
average  and  apparently  here,  also,  a  test  score  gives  about  the  same 
accuracy  of  prediction  as  does  a  high-school  mark.  Perhaps  the  most 
important  conclusion  is  that  the  whole  problem  needs  much  more  care- 
ful and  extensive  investigation,  especially  along  the  line  of  finding  the 
best  type  or  types  of  entrance  examinations  covering  the  high-school 
subjects  and  of  combining  the  results  therefrom  with  other  data  to  give 
the  best  multiple  predictions  possible. 


[19] 


CHAPTER  III 

THE  GENERAL  PLAN  OF  THIS  STUDY 

The  initial  collection  of  high-school  data.  The  data  used  in  this 
investigation  concern  a  group  of  individuals  graduated  from  several  hun- 
dred high  schools  in  the  state  of  Illinois  in  1924  and  admitted  to  various 
institutions  of  higher  learning  in  the  summer  or  autumn  of  the  same 
year.  In  the  fall  of  1923  all  the  four-year  public  high  schools  in  the 
state  were  invited  to  cooperate  with  the  Bureau  of  Educational  Research 
in  this  study.  The  number  that  did  so  was  368,  a  few  more  than  one-' 
half  of  all  those  within  the  state,  and  the  number  of  seniors  included 
was  about  12,300.  The  data  secured  concerning  them  consisted  of  their 
scores  upon  the  Otis  Self- Administering  Test  of  Mental  Ability,  Higher  j 
Examination,  Form  A  and  the  answers  to  the  questions  on  an  "Informa- 
tion Blank  for  High-School  Seniors,"  which  called  for  the  following  in-j 
formation : 

Name 

Sex 

Date  of  Birth 

Age  on  September  1,  1923 

Name  of  school 

Town  or  city 

Intentions  concerning  further  education 

Intention  of  continuing 

Institution 

Course 

Major    subject 

Vocational  choice 

Father's  occupation 

Information  as  to  previous  intelligence  tests  taken 

Units  of  high-school  credit 

High-school  subjects  liked  most 

High-school  subjects  liked  least 

Number  of  failures  in  high  school 

Average  high-school  mark^ 

The  tests  were  given  by  principals  or  by  teachers  designated  by  them] 
and  the  information  blanks  filled  out  by  the  seniors  themselves.     All 
scoring  of  test  papers  and  tabulation  of  results  was  done  in  the  offices^ 
of  the  Bureau  of  Educational  Research. 


^This  was  the  average  mark  up  to  date  or  for  the  first  three  years.    It  was  secured] 
from  only  a  minority  of  the  schools  and  for  about  2700  seniors. 


[20] 


The  second  step  in  collecting  high-school  data.  A  year  later,  In 
the  fall  of  1924.  the  368  high  schools  were  asked  to  furnish  the  complete 
high-school  scholastic  records  of  all  pupils  for  whom  the  other  Informa- 
tion had  been  secured,  and  also  If  possible,  to  state  what.  If  any,  Insti- 
tution of  higher  learning  each  Individual  was  attending.  A  few  of  the 
seniors  of  the  year  before  had  not  been  graduated,  and  In  a  few  cases 
the  desired  records  were  not  forthcoming,  but  the  loss  from  these 
sources  was  comparatively  slight,  so  that  the  complete  scholastic  high- 
school  records  of  about  11,500  graduates  were  secured.  Since  these 
marks  came  from  several  hundred  schools  which  employed  a  total  of 
over  one  hundred  different  marking  systems,  if  all  minor  variations  be 
counted,  it  was  necessary  to  transmute  them  to  a  uniform  basis.  For 
this  purpose  a  percentile  system  with  passing  at  70  and  no  conditions 
was  chosen.  The  marks  given  according  to  all  other  plans  were  changed 
to  this  system  by  approved  and  careful  statistical  procedure. 

The  collection  of  college  freshman  data.  Some  three  hundred 
institutions  of  higher  learning  had  been  named  by  the  seniors  In  answer 
to  the  question  as  to  where  they  expected  to  continue  their  education. 
Early  in  the  academic  year  of  1925-26  letters  were  addressed  to  all  these 
institutions  asking  for  the  complete  1924-25  scholastic  records  of  all 
freshmen  coming  from  any  of  the  high  schools  Included  In  this  study. 
About  7,700  of  the  seniors  had  stated  that  they  intended  to  continue 
their  education.  In  addition  to  many  who  were  undecided,  and  the  ma- 
jority of  them  had  named  the  Institutions  they  expected  to  attend.  De- 
spite this  fact  the  freshman  records  of  not  quite  two  thousand  students 
were  all  that  were  secured.  This  loss  is  due  to  at  least  four  causes.  In 
the  first  place,  a  number  of  the  collegiate  institutions  addressed  either 
were  unwilling  to  cooperate  in  the  study,  or,  after  expressing  their  will- 
ingness to  do  so,  failed  to  send  the  desired  records.  A  second  reason 
was  that  a  number  of  the  Institutions  which  did  cooperate  failed  to  fur- 
nish the  data  for  all  of  their  students  for  whom  they  were  desired. 
Third,  undoubtedly  many  of  the  high-school  graduates  who  planned  to 
attend  college  found  It  necessary,  for  financial  or  other  reasons,  to  post- 
pone entrance  for  a  year  or  more  after  high-school  graduation.  The 
last,  and  probably  the  most  Important,  reason  was  the  fact  that  In  filling 
out  the  Information  blanks  the  high-school  seniors  expressed  their  high- 
est hopes  and  ambitions  or  gave  answers  which  they  thought  would 
sound  best  and  that,  therefore,  many  of  them  who  had  very  slight  ex- 
pectations of  ever  actually  attending  college,  signified  that  they  intended 
to  do  so. 


[21] 


Of  the  approximately  two  thousand  students  whose  records  were 
secured  from  various  colleges,  almost  one  hundred  did  not  remain  in 
college  long  enough  to  have  any  marks  recorded.  The  number  for 
whom  marks  for  at  least  one  quarter,  term,  or  semester  were  secured 
was  1892,  and  for  1677  of  these  a  full  year's  marks  were  obtained.  As 
these  marks  were  given  by  more  than  one  hundred  institutions  it  was 
necessary  to  transmute  them  to  a  common  basis  in  the  same  manner 
as  had  been  done  for  the  high-school  marks,  and  so  all  were  adjusted 
to  the  same  basis  of  a  percentile  marking  system  with  70  as  passing 
and  no  conditions. 

The  reliability-  of  the  data  secured  in  this  investigation.  There 
is  no  doubt  that  in  both  intelligence  test  scores  and  high-school  and  col- 
lege marks  large  variable  errors  are  present.  No  group  intelligence  test 
so  far  devised  yields  highly  accurate  individual  scores  and  the  Otis 
Self-Administering  Test,  which  requires  only  half  an  hour  to  give,  is 
probably  less  reliable  than  one,  such  as  the  Thorndike  Intelligence  Ex- 
amination, which  consumes  two  or  three  hours.  Moreover,  the  tests 
were  not  administered  by  a  corps  of  trained  and  selected  examiners,  but 
by  several  hundred  different  principals  and  teachers,  many  of  whom  had 
probably  never  given  a  standardized  test.  This  fact  undoubtedly  served 
to  increase  the  errors  in  the  scores.  It  should  not  be  overlooked,  how- 
ever, that  the  test  used  reduces  the  directions  to  be  given  by  examiners 
to  a  minimum  and  that,  therefore,  the  errors  due  to  lack  of  training  of 
the  persons  giving  the  tests  are  less  than  would  otherwise  be  the  case. 
The  writer  does  not  believe,  however,  that  this  factor  of  added  reliability 
is  sufficient  to  balance  the  two  of  brevity  and  administration  by  poorly 
qualified  examiners  which  make  for  the  opposite  effect. 

The  method  of  computing  intelligence  quotients,  which  Otis  pro- 
vides, introduces  a  constant  error  into  many  of  those  so  determined.^ 
However,  as  little  use  will  be  made  of  the  I.  Q.  in  the  discussion,  it 
does  not  seem  worth  while  to  discuss  this  point  further  than  to  call 
attention  to  the  fact' that  the  coefficients  of  correlation  between  the  I.  Q. 
and  other  data  are  probably  slightly  lower  than  they  should  be  and. 


"As  used  in  this  bulletin,  the  term  '"reliability"  is  practically  equivalent  to  "ac- 
curacy." It  is  not  limited  to  its  sometime  narrow  technical  meaning  referring  to  the 
agreement  between  two  sets  of  scores  on  the  same  measuring  instrument,  though  it 
includes  this. 

'For  a  more  complete  discu,ssion  of  this  point,  see: 

Odell,  C.  W.  "Are  college  students  a  select  group?"'  University  of  Illinois  Bulle- 
tin, Vol.  24,  Xo.  36,  Bureau  of  Educational  Research  Bulletin  No.  34.  Urbana:  Uni- 
versity of  Illinois,  1927,  p.  16-17. 


[22] 


therefore,  the  estimated  accuracy  of  predictions  made  on  the  basis  of 
the  I.  Q.  is  also  sHghtly  too  low. 

An  additional  fact  which  probably  affected  the  significance  of  the 
test  scores  was  that  about  half  of  the  seniors  tested  had  never  taken 
an  intelligence  test  before  and  it  is  likely  that  many  of  their  scores, 
when  compared  with  most  of  those  of  the  seniors  who  had  taken  such 
tests  previously,  do  not  fairly  represent  their  mental  ability.  Further- 
more, because  of  the  conditions  under  which  the  tests  were  given,  there 
was  generally  no  particular  incentive,  apart  from  the  desire  to  excel, 
for  the  pupils  to  do  their  best.  Hence,  it  is  likely  that  a  considerable 
number  of  them  did  not  put  forth  maximum  effort  while  taking  the 
test.  These  and  all  other  causes  which  produce  variable  or  accidental 
errors  in  the  test  scores  result  in  lowering  the  correlations  and  other 
predictive  indices  based  thereon  and  justify  the  conclusion  that  the. 
real  relationships  are  somewhat  closer  than  those  actually  computed. 

Too  much  evidence  and  discussion  concerning  the  subjectivity  and 
unreliability  of  school  marks  has  appeared  within  the  last  few  years 
for  the  subject  to  need  extended  comment  In  this  connection.  Undoubt- 
edly the  errors  present  in  the  marks  were  Increased  somewhat  by  the 
fact  that  marks  from  several  hundred  high  schools  and  more  than  a 
hundred  colleges  with  different  systems  and  standards  were  transmuted 
to  a  common  basis  and  thrown  into  a  single  group.  In  spite  of  the  fact 
that  the  transmutation  was  made  with  great  care  and  followed  sound 
statistical  procedure,  it  was  not  possible.  In  all  cases,  to  be  sure  that 
the  transmuted  marks  were  really  equivalent  to  the  original  ones.  The 
effect  of  increasing  such  variable  errors  was  to  lower  the  coefficients  of 
correlation  and  other  predictive  measures  secured. 

The  computation  of  zero-order  coefficients  of  correlation.  As  has 
been  suggested,  the  chief  method  employed  In  determining  the  relation- 
ships existing  between  college  freshman  marks  and  the  other  data  avail- 
able was  that  of  correlation.  It  was  found  that  there  were  forty-nine 
subjects  or  closely  related  groups  of  subjects*  each  of  which  had  been 
carried  by  ten  or  more  freshmen.  Correlation  tables  were  made  for  the 
mark  in  each  of  these  subjects  or  subject  groups  with  age,  mental  test 
score,  intelligence  quotient,  general  high-school   average,  and  average 


^In  a  number  of  cases  it  is  doubtful  just  what  really  constitutes  a  "subject"  as 
the  term  is  commonly  used.  This,  for  example,  is  true  of  agriculture.  In  cases  in 
which  there  were  only  a  few  freshmen  who  carried  each  of  the  several  possible  divisions 
the  procedure  followed  was  to  group  them  together  as  a  single  subject.  Agriculture, 
therefore,  includes  various  courses  in  agronomy,  animal  husbandry,  and  so  forth;  art 
includes  freehand  drawing,  painting  and  sculpture,  and  so  on  with  others. 


[23] 


mark  in  each  high-school  subject  or  group  of  subjects  with  which  it 
seemed  Hkely  that  there  was  close  relationship.  Thus,  for  example, 
college  freshman  biology  mark  was  correlated  with  marks  in  high-school 
biology,  botany,  general  science,  and  zoology  and  also  with  the  average 
mark  in  all  high-school  science.  Likewise,  that  in  French  was  corre- 
lated with  high-school  English,  French,  Latin,  and  Spanish  marks,  and 
also  with  the  general  high-school  foreign  language  average. 

In  addition  to  these  correlations  quite  a  number  were  made  be- 
tween the  freshman  marks  and  the  amounts  of  time  devoted  to  partic- 
ular subjects  or  groups  of  subjects  in  high  school  and  also  between 
freshman  marks  and  those  in  the  work  of  particular  years  in  high 
school.  For  example,  the  freshman  biology  mark  was  correlated  with 
the  number  of  semesters  of  biology  carried  in  high  school,  also  with 
•the  total  number  of  semesters  of  science  carried.  The  freshman  French 
mark  was  correlated  with  the  number  of  semesters  of  high-school 
French,  of  high-school  Latin,  and  of  all  high-school  foreign  language, 
also  with  the  marks  in  first,  second,  third,  and  fourth  year  Latin  and 
French,  in  so  far  as  each  had  been  carried.  After  such  correlation 
tables  had  been  made  for  a  dozen  or  more  of  the  freshman  subjects  it 
appeared  that  the  results  therefrom  would  contribute  nothing  of  value 
to  the  study,  so  no  more  were  constructed.  The  correlations  of  fresh- 
man marks  with  the  amounts  of  particular  subjects  and  groups  of  sub- 
jects carried  in  high  school  were  so  near  zero  as  to  offer  no  help  in 
predicting  freshman  marks.  The  correlations  with  a  particular  year's 
work  in  high  school  were  higher,  but  they  appeared  to  add  nothing  not 
already  contributed  by  those  of  freshman  marks  with  marks  in  all  the 
high-school  work  in  the  various  subjects.  In  some  cases  they  were 
practically  as  high  as  the  latter,  but  the  use  of  the  multiple  correlation 
procedure  showed  that  they  added  almost  nothing  In  accuracy  of  pre- 
diction. 

After  constructing  the  tables  described,  the  next  step  was  naturally 
to  compute  the  simple  or  ordinary  coefficients  of  correlation  for  them. 
It  should  be  remembered  that,  since  many  of  these  correlations  involve 
as  one  variable  an  average  mark  for  a  group  of  similar  high-school  sub- 
jects or  for  all  high-school  subjects,  the  coefficients  obtained  from  them 
are  in  a  sense  multiple  coefficients  although  not  obtained  by  the  multiple 
correlation  method.  In  other  words,  they  show  the  relationship  existing 
between  college  freshman  marks  and  combinations  of  several  different 
high-school  marks. 

The  computation  of  coefficients  of  multiple  correlation  and  re- 
gression.   The  calculation  of  zero  order  or  simple  coefficients  of  corre- 

[24] 


latlon  was  followed  by  that  of  multiple  coefficients  and  regression  equa- 
tions. In  view  of  the  considerable  amount  of  labor  involved  in  comput- 
ing the  latter  they  were  not  found  for  all  freshman  subjects,  but  for 
only  about  one-third  of  them.  These  were  in  general  the  subjects  carried 
by  the  largest  numbers  of  freshmen  and  two  or  three  others  included 
because  of  especial  interest  in  them.  In  connection  with  this  the  admis- 
sion should  be  made  that  since  many  possible  correlations  were  not  com- 
puted it  is  probable  that  some  were  omitted  which  should  have  been 
found.  Since  the  amount  of  money  available  for  clerical  help,  though 
fairly  generous,  was  not  unlimited,  it  was  necessary  that  the  line  be 
drawn  somewhere,  and  it  is  very  likely  that  the  writer's  judgment  in  se- 
lecting the  most  promising  possibilities  was  not  infallible.  In  the  case  of 
several  of  the  freshman  subjects  two  or  three  groupings  were  made  ac- 
cording to  the  high-school  subjects  carried  and  a  different  set  of  multi- 
ple correlations  computed  for  each  grouping.  For  example,  in  addition 
to  calculating  the  correlations  and  regressions  for  all  freshmen  who  car- 
ried Latin  as  a  college  freshman  subject,  they  were  also  found  separateh' 
for  the  portion  of  this  group  that  had  carried  high-school  French.  The 
general  procedure  in  computing  the  multiple  coefficients  was  to  start 
with  the  highest  one  of  zero  order  and  combine  the  others  of  the  same 
order  with  it  until  the  addition  of  another  criterion  no  longer  increased 
the  obtained  coefficient  by  as  much  as  .01.  Because  of  the  fact  referred 
to  above,  that  many  of  the  simple  coefficients  of  correlation  were  really 
multiple  in  nature  though  not  in  derivation,  it  could  not  be  expected 
that  on  the  whole  there  would  be  as  great  an  increase  in  the  multiple 
coefficients  over  those  of  zero  order  as  would  otherwise  have  been  the 
case. 

The  question  may  be  raised  as  to  why  certain  combinations,  which 
will  appear  later  in  the  chapter  containing  the  multiple  correlation  re- 
sults, were  made,  in  view  of  the  fact  that  one  of  the  simple  correlations 
already  used  was  that  of  the  freshman  mark  with  the  general  high-school 
average  or  the  average  in  a  group  of  similar  subjects,  and  another  the 
correlation  with  one  of  the  subjects  which  entered  into  this  group.  For 
example,  the  highest  obtained  multiple  coefficient  for  freshman  rhetoric 
was  that  obtained  from  a  combination  of  high-school  average,  high- 
school  English  mark,  and  point  score  on  the  test,  and  of  course  the  high- 
school  average  included  the  high-school  English  mark.  The  reason  for 
so  doing  is,  however,  clear  to  any  one  familiar  with  multiple  correlation. 
In  computing  the  high-school  general  average  or  the  average  in  any 
group  of  similar  subjects  the  marks  entering  into  the  given  average 
were  all  allowed  the  same  weight  in  determining  it.    By  means  of  mul- 

[  -'5  ] 


tiple  regression  equations,  however,  one  is  able  to  determine  the  opti- 
mum weight  which  should  be  given  to  each  factor,  that  is,  the  weight  to 
give  it  so  that  the  highest  correlation  or  predictive  power  will  be  ob- 
tained. Therefore,  the  fact  that  a  combination  of  high-school  English 
mark  and  the  high-school  general  average  resulted  in  a  higher  correla- 
tion with  freshman  rhetoric  than  did  the  former  alone,  merely  means 
that  the  weighting  of  English  equally  with  other  subjects  in  computing 
the  general  average  is  not  high  enough  to  yield  the  best  prediction  and, 
therefore  if  it  is  only  given  equal  weighting  with  the  other  subjects  in 
this  average,  it  should  be  introduced  again  with  the  relative  weight  in- 
dicated by  the  multiple  regression  coefficient  to  accomplish  this  purpose. 
The  direct  method  of  securing  the  same  result  would  be  to  use  no 
averages  of  marks  in  different  high-school  subjects,  but  to  consider  each 
as  a  separate  variable  or  criterion  in  the  multiple  correlation  work.  The 
reason  this  was  not  done  was  that  it  would  have  increased  very  greatly 
the  amount  of  calculation  necessary  without  yielding  more  helpful  re- 
sults than  the  method  used.  It  would,  of  course,  have  shown  exactly 
just  which  of  the  subjects  entering  into  the  high-school  average  were 
useful  for  making  the  best  prediction  in  each  case  and  which  were  not. 
but  there  seems  little  advantage  in  knowing  this,  provided  one  knows 
how  to  make  as  good  an  estimate  without  this  knowledge  and  with  even 
less  labor.  Xot  only  was  much  work  saved  in  computation,  but  also  in 
the  use  of  results,  since  the  multiple  coefficients  and  regression  equa- 
tions secured  involve,  on  the  whole,  fewer  variables  or  criteria  than 
would  be  the  case  if  averages  of  high-school  subjects  had  not  been  taken 
and  therefore  require  less  computation  in  employing  them  for  predic- 
tive purposes.  The  objection  can  be  raised  that  there  are  included  In  the 
general  high-school  average  marks  made  in  subjects  which  show  much 
lower  correlations  with  the  freshman  subject  being  considered  than  do 
those  of  certain  other  high-school  subjects  and  that  the  inclusion  of 
these  marks  may  have  lowered  the  correlation  between  the  freshman 
subject  mark  and  the  high-school  average.  This  contention  Is  true,  but 
the  writer  believes  that  for  all  practical  purposes  any  such  results  have 
been  taken  care  of  by  including  in  the  multiple  correlations  and  regres- 
sions the  subjects  which  appeared  at  all  likely  to  make  any  contribution 
to  them.  Thus,  for  example,  if  freshman  French  mark  was  best  pre- 
dicted by  a  combination  of  high-school  marks  In  English,  French  and 
Latin  and  point  score,  rather  than  by  Including  the  general  high-school 
average,  the  method  of  computation  used  eliminated  the  latter.  In  any 
event,  In  view  of  the  practical  limitations  of  time  and  money,  It  seemed 
wise.  If  not  absolutely  necessary,  to  follow  the  method  described  above. 

[26] 


The  measures  of  accuracy  of  prediction  obtained  in  this  study. 

Finally,  as  a  measure  of  the  accuracy  or  reliability  of  predictions  based 
upon  coefficients  of  correlation  and  regression  equations,  the  coeffi- 
cients of  alienation  and  the  probable  errors  of  estimate  corresponding  to 
each  of  the  former  expressions  were  determined.  The  first  of  these, ^  the 
coefficient  of  alienation,  is  an  expression  which  shows  the  relationship 
between  the  prediction  based  upon  a  given  coefficient  of  correlation  and 
a  pure  guess.  For  example,  the  coefficient  of  alienation  which  corre- 
sponds to  a  correlation  coefficient  of  .65  is  approximately  .76.  This 
means  that  if  two  variables  or  series  of  scores  correlate  .65  with  each 
other,  the  estimates  of  particular  scores  in  one  series  based  upon  corre- 
sponding known  scores  in  the  other  will  on  the  average  be  in  error  by 
about  .76  as  much  as  if  the  errors  resulted  from  pure  guesses,  or,  sub- 
tracting .76  from  1.00,  that  the  errors  will  be  .24  smaller  than  those  in 
pure  guesses. 

The  probable  error  of  estimate  describes  the  same  situation  by 
stating  the  limits  within  which  half  of  the  errors  will  fall.  For  example, 
If  the  probable  error  of  estimate  Is  found  to  be  4  points  on  a  percentile 
scale.  It  means  that  half  of  the  estimated  scores  will  not  vary  from  the 
true  scores  by  more  than  4  per  cent,  and,  of  course,  that  the  other  half 
will  differ  by  more  than  this  amount.  These  two  indices,  the  coefficient 
of  alienation  and  the  probable  error  of  measurement,  give  a  more  con- 
crete and  meaningful  description  of  the  accuracy  of  prediction  than  does 
the  coefficient  of  correlation. 


°For  a  more  complete  discussion  of  the  coefficient  of  alienation  and  the  probable 
error  of  estimate,  see  Chapter  VI.   Also: 

Odell,  C.  W.  "The  interpretation  of  the  probable  error  and  the  coefficient  of  cor- 
relation." University  of  Illinois  Bulletin,  Vol.  23,  No.  52,  Bureau  of  Educational  Re- 
search Bulletin  No.  32.    Urbana:  University  of  Illinois,  1926,  p.  28-32  and  41-45,  and 

Odell,  C.  W.  Educational  Statistics.  New  York:  The  Century  Company,  1925, 
p.  173-74,  230-41,  or  some  other  text  on  the  same  subject. 

[27] 


CHAPTER  IV 

THE  SIMPLE  CORRELATIONS  BETWEEN  FRESHMAN 
MARKS  AND  THE  OTHER  DATA  COLLECTED 

The  simple  correlations  computed  in  this  study.    At  the  risk  of 

repeating  a  portion  of  the  outHne  of  the  study  given  in  the  last  chap- 
ter, it  seems  worth  while  to  state  again  what  correlations  were  and  were 
not  found.  The  simple  or  zero-order  coefficients  obtained  are  shown  in 
Table  III,  the  first  column  of  which  gives  the  correlations  of  the  fresh- 
man marks  with  age,  the  second  those  with  point  score,  the  third  with 
I.  Q.,  and  the  fourth  with  the  general  high-school  average.  Following 
this  are  the  coefficients  found  between  the  marks  in  various  freshman 
subjects  and  those  in  high-school  subjects  or  groups  of  subjects  selected 
as  being  most  similar  to  the  freshman  ones,  or  as  most  likely  to  ex- 
hibit significant  correlations  with  them.  Thus,  for  example,  the  first  row 
of  the  table  shows  that  freshman  accountancy  mark  had  a  correlation 
of  — .18  with  age,  .28  with  point  score,  .29  with  I.  Q.,  .47  with  high- 
school  average,  .38  with  high-school  commercial  average  and  .47  with 
high-school  mathematics  average.  As  was  mentioned  in  Chapter  III. 
correlation  coefficients  between  certain  possible  criteria  and  college 
marks  are  not  included  in  this  table  because,  after  computing  quite  a 
number  of  them,  it  appeared  that  they  were  of  so  little  value  for  the 
purpose  of  this  investigation  as  not  to  be  worth  further  consideration. 
These  were  the  coefficients  of  the  freshman  subject  marks  with  the 
amounts  of  particular  subjects  carried  in  high  school  and  with  particular 
years'  marks  in  high-school  subjects,  rather  than  with  the  average  for 
all  of  each  subject.  It  will  be  noted  that  a  number  of  the  coefficients 
given  in  Table  III  are  enclosed  in  parentheses.  These  are  the  ones 
which,  because  of  the  joint  effect^  of  their  small  size  and  the  few  cases 
concerned,  are  less  than  twice  their  standard  errors  or  three  times  their 
probable  errors  and  so  can  hardly  be  considered  reliable.  The  chances 
are  greater  than  twenty-one  or  twenty-two  to  one  that  all  of  the  co- 


1— r" 
^The  formula  for  the  standard  error  of  a  coefficient  of  correlation  is  — 7^    and 

VN 

that  for  the  probable  error  .6745      ,—.,  in  which  r  is  the  coefficient  of  correlation  and 

N  the  number  of  cases.  Thus  the  greater  the  Coefficient  and  also  the  greater  the 
number  of  cases  the  smaller  is  the  error  and  the  greater  the  reliability  of  the  coeffi- 
cient. 

[28] 


b 


INT  SC( 


3L  SUBJI 


French 


A\ 

Al 

Al\l 

Ar 

Arl 

Atl 

Bil 


.46 


,50 


.60 


ree   times  their 


■r. 

LEm 

coEr 

P,aE> 

TSOF 

COHRK.Ar.0 

VOFF 

RESHJ 

RKSU 

T„« 

h5,  1'  )1NT  SCORES. 

NTELLIGEN'CE  QUOTIENTS 

.,ND 

■IIGH-SCHOOL 

1 

,,J, 

s 

I.Q, 

SCHO  )L  SUBJECTS  AND  GROUPS  OE  SUBJECTS 

Av„. 

A,n- 

AlE- 

fln.h^ 

Sr, 

B,ol- 

Bo,- 

Ck.m- 

Civ- 

Com- 

Eco„- 

En- 

ri": 

FrrnrI, 

Hi>. 

Homt 

"It 

M.ih- 

Mak- 

Hu-i. 

Phy.. 

Vab. 

Sci- 

Sp.n- 

Eod- 

' 

17 

30 

-^ 

tory 

omics 

Train. 

ks 

ing 

'" 

Sp^t. 

ence 

ogy 

s 

.4. 

r 

' 

. 

. 

.. 

(   171 

1 

.« 

.» 

« 

3, 

.SO 

(.2?) 

.. 

.2.1 

I  0.1) 

.» 

(  3S) 

,-    ».., 

.„ 

,,» 

' 

.52 

.60 

(14) 

" 

(  .11) 

z 

.2, 

(-   24) 

(.40) 

:,; 

.40 

(.4-1) 

"" 

'"  ""' 

"  '"  '"'■' 

"'  ""'  ' 

:n."i 

"""'  ''" 

■''"'■ 

1 

efficients  not  in  parentheses  are  significant  or  reliable  and  for  most  of 
them  the  chances  are  very  much  greater  than  this. 

The  correlations  between  freshman  marks  and  age.  A  glance  at 
the  first  column  of  the  table  shows,  that,  as  one  would  expect,  most  of 
the  correlations  with  age  are  negative.  In  fact  none  of  the  few  small 
positive  ones  are  reliable  and  the  smallest  reliable  negative  one  is  — .11 
for  economics.  Others  close  to  this  are  those  for  chemistry  and  history. 
From  this  point  they  range  up  to  — .44  for  philosophy,  the  only  others 
greater  than  — .30  being  for  botany  and  physiology.  The  correlation  of 
the  general  freshman  average  with  age  is  —.23.  Although  about  half 
the  coefficients  in  this  column  are  reliable  and  therefore  indicate  that 
there  is  a  definite  inverse  relationship  between  age  and  freshman  marks, 
they  are  so  small  as  to  offer  practically  no  assistance  In  predicting  the 
quality  of  freshman  work  when  age  alone  Is  known.  Later,  In  Chapter 
VI,  the  question  of  just  how  much  relationship  is  indicated  by  coeffi- 
cients of  correlation  of  given  sizes  will  be  discussed  and  thus  the  mean- 
ing of  these  and  the  others  obtained  In  this  study  made  more  concrete. 
For  the  present  it  Is  sufficient  to  say  that  the  only  prediction  justified 
upon  the  basis  of  age  is  that  there  Is  a  very  slight  tendency  for  fresh- 
men who  are  below  the  average  age  of  their  group  to  do  better  work 
than  Is  done  by  those  above  the  average  age. 

The  correlations  of  freshman  marks  with  point  scores  and  intelli- 
gence quotients.  An  inspection  of  columns  two  and  three  of  the  table 
reveals  what  anyone  familiar  with  the  situation  would  anticipate,  that 
in  most  cases  the  entries  in  the  two  columns  are  very  nearly  the  same, 
the  only  exceptions  being  In  cases  where  the  coefficients  are  too  small  to 
be  reliable.  In  other  words,  because  of  the  fact  that  the  point  score  Is 
one  of  the  two  factors  upon  which  the  I.  Q.  directly  depends,  the  corre- 
lations of  any  other  variable  except  age,  which  Is  the  second  factor,  with 
these  two  are  very  likely  to  be  the  same  or  almost  the  same.  The  writer 
seriously  considered  the  advisability  of  not  computing  any  correlations 
with  the  I.  Q.,  but  did  so  to  try  to  determine  whether,  on  the  whole, 
it  makes  any  difference  at  all  which  one  of  the  two  is  used.  By  looking 
at  the  columns  it  will  be  seen  that  sometimes  one  and  sometimes  the 
other  Is  the  larger  and  that  the  coefficients  of  both  with  the  general 
freshman  average  are  .38.  Thus  It  appfears  that  from  the  standpoint  of 
prediction  it  makes  no  difference  which  one  is  used.  From  the  practical 
standpoint,  however,  It  seems  clear  that  the  point  score  should  be  used 
since  the  calculation  of  the  I.  Q.  Involves  an  additional  step. 

It  will  be  seen  that  all  of  the  correlations  between  freshman  marks 
and  test  results  are  positive  except  in  the  case  of  athletic  coaching  and 

[29] 


that  here  they  are  not  reliable.  The  smallest  ones  possessing  reliability 
are  those  for  mechanical  drawing  and  physical  education,  which  are  about 
.16.  Other  rather  low  ones  at  or  below  .25  are  those  for  art.  biology, 
hygiene,  and  industrial  arts.  In  addition  to  these  a  number  of  those  in 
parentheses,  in  fact  almost  all  of  them,  are  small.  The  closest  relation- 
ship between  freshman  marks  and  test  results  appears  to  be  in  the  case 
of  pharmacy  for  which  the  coefficients  are  slightly  above  .50.  Other 
subjects  with  coefficients  above  .40  are  arithmetic,  botany,  commerce, 
engineering,  music  theory,  physiology,  and  psychology. 

Table  III  and  the  discussion  just  above  indicate  that  there  is  a 
closer  relationship  between  score  on  the  test  used  and  freshman  marks 
than  between  age  and  such  marks.  It  may  be  said  that  the  degree  of 
relationship  is  about  twice  as  close  in  the  sense  that  it  is  twice  as  far 
away  from  zero  correlation  or  no  relationship  at  all.  A  test  score,  there- 
fore, offers  a  better  basis  of  predicting  success  in  freshman  college  work 
than  does  an  age,  but,  as  will  be  shown  in  more  detail  in  Chapter  \T,  it 
cannot  be  said  to  be  very  satisfactory  for  that  purpose.  Even  in  the  case 
of  pharmacy,  which  exhibited  the  closest  relationship,  estimates  of  fresh- 
man marks  based  upon  test  scores  would  be  only  15  per  cent  better  than 
pure  guesses,  whereas  for  the  freshman  average  they  would  be  only 
about  7^4  per  cent  better.  The  corresponding  figures  for  age  are  about 
10  per  cent  better  for  philosophy,  which  has  the  largest  negative  coeffi- 
cient, and  less  than  3  per  cent  better  for  the  freshman  average.  Thus  the 
most  favorable  statement  which  can  be  made  about  predicting  freshman 
marks  from  the  mental  test  scores  secured  in  this  study  is  only  slight!}' 
stronger  than  that  made  above  concerning  the  use  of  age  for  the  same 
purpose.  There  is  a  positive,  but  not  very  strong,  tendency  for  those 
who  made  high  scores  on  the  test  also  to  make  high  freshman  marks. 

The  correlations  of  freshman  marks  with  the  high-school  average. 
The  entries  in  the  fourth  column  of  the  table,  which  are  the  coefficients 
between  the  freshman  marks  and  the  general  high-school  average,  are, 
on  the  whole,  higher  than  those  in  the  preceding  columns.  Two  of  those 
in  parentheses  are  negative  and  the  smallest  reliable  one,  .15  for  physical 
education,  is  just  about  the  same  as  the  smallest  for  point  score  or  I.  Q. 
Others  below  .20  are  those  for  mechanical  drawing  and  military.  On 
the  other  hand,  however,  there  are  a  number  of  these  coefficients  greater 
than  .50  and  two  above  .60  as  compared  with  only  one  for  point  score 
and  I.  Q.  above  .50.  The  two  referred  to  as  being  above  .60  are  .69  for 
dentistry  and  .62  for  horticulture.  Others  between  .50  and  .60  were 
found  in  the  cases  of  agriculture,  botany,  French,  Latin,  philosophy, 
physiology,  Spanish,  and  zoology.    The  correlation  between  the  high- 

[30]  ^^ 


school  and  the  freshman  averages  is  .55,  ahnost  half  again  as  large  as 
that  of  the  latter  with  test  results. 

Despite  the  decided  increase  in  the  size  of  the  coefficients,  the  ac- 
curacy of  prediction  based  upon  high-school  averages  is  still  not  at  all 
high.  For  a  coefficient  of  .69,  such  as  is  possessed  by  dentistry,  a  pre- 
diction is  only  about  28  per  cent  better  than  a  pure  guess  and  for  one  of 
.55,  such  as  that  for  the  freshman  average,  it  is  about  16  per  cent  bet- 
ter. In  other  words,  just  as  the  improvement  over  no  predictive  power 
at  all  is  roughly  twice  as  great  for  the  test  scores  as  it  is  for  ages,  so  also 
it  Is  about  twice  as  great  for  high-school  averages  as  for  test  scores. 
There  is  no  question  but  that  with  a  few  exceptions  much  better  predic- 
tions of  probable  freshman  marks  could  be  based  upon  the  high-school 
averages  than  upon  the  test  scores  obtained  in  this  study.  The  most 
marked  exceptions  to  this  were  in  the  case  of  art,  commerce,  and  phar- 
macy, although  in  arithmetic,  engineering,  music  theory,  and  physical 
education  the  correlations  of  freshman  marks  with  the  test  score  were 
also  slightly  higher  than  those  with  the  high-school  average. 

The  correlations  between  freshman  marks  and  those  in  single 
high-school  subjects  or  groups  of  subjects.  The  part  of  Table  III  to 
the  right  of  the  column  headed  "Average"  shows  the  coefficients  be- 
tween the  freshman  subject  marks  and  those  in  particular  high-school 
subjects  or  groups  of  subjects.  The  number  for  the  different  freshman 
subjects  varies  from  one  to  eight,  but  in  no  case  are  there  more  than  five 
of  the  coefficients  for  a  single  subject  which  are  significant.  Glancing 
over  them  one  sees  that  with  the  exception  of  two  or  three  of  those  in 
parentheses  none  are  negative  and  that  the  reliable  ones  range  from  .23 
up  to  .87.  The  one  of  .87,  between  freshman  zoology  and  high-school 
botany  mark,  is  based  on  a  small  number  of  cases  and  although  it  is 
much  more  than  three  times  its  probable  error,  probably  should  not  be 
considered  as  having  high  reliability.  The  next  In  size  is  one  of  .65  be- 
tween freshman  philosophy  and  high-school  English  mark  which,  al- 
though not  based  on  a  very  large  number  of  cases,  can  still  probably  be 
considered  fairly  reliable.  The  only  others  as  high  as  .60  are  those  of 
I  freshman  horticulture  mark  with  that  in  all  high-school  science,  fresh- 
man Spanish  with  high-school  French  and  freshman  stenography  with 
high-school  commercial  work,  of  which  only  the  second  is  based  on  a 
large  number  of  cases,  although  the  other  two  are  more  than  three 
times  their  probable  errors.  It  will  be  seen  that  the  central  tendency  of 
these  coefficients  is  around  .40,  about  two-thirds  of  them  being  between 
.30  and  .50. 

[31] 


In  view  of  the  irregularity  in  the  size  of  the  coefficients,  it  is  rather 
difficult  to  say  that  many  high-school  subjects  or  groups  of  subjects  are 
on  the  whole  of  more  value  in  predicting  freshman  marks  because  they 
correlate  more  closely  with  them,  than  are  others.  French,  however, 
may  be  pointed  out  as  probably  the  most  useful  in  this  connection,  since 
it  correlates  with  freshman  French  almost  as  highly  as  does  the  general 
foreign  language  average,  with  freshman  Latin  almost  as  highly  as 
does  English,  and  with  freshman  Spanish  eight  points  more  highly  than 
any  other  subject  or  group  of  subjects.  Thus  on  the  whole  it  furnishes 
a  better  prediction  of  success  in  Latin  and  the  two  languages  derived 
from  it  than  does  Latin  itself  or  the  whole  high-school  foreign  language 
average.  High-school  English,  also,  on  the  whole  correlates  fairly  closely 
with  a  number  of  freshman  subjects,  though  in  some  cases  the  coeffi- 
cients fall  below  .40. 

Looking  through  the  table  carefully  one  will  see  that  in  the  case  of 
almost  every  freshman  subject  the  correlation  with  some  one  high- 
school  subject  or  group  of  subjects  is  higher  than  that  with  the  high- 
school  average  and  also  with  age,  point  score  or  1.  Q.  In  most  cases, 
however,  it  is  not  much  greater  than  that  with  the  high-school  average. 
This  difference,  however,  warrants  the  conclusion  that  if  simple  correla- 
tion alone  is  to  be  used  in  predicting  success  in  freshman  subjects,  it 
will  in  most  cases  be  unnecessary  to  secure  age  records,  scores  on  the 
mental  test  used  in  this  study,  or  even  the  general  high-school  average, 
but  that  the  high-school  mark  in  the  subject  or  group  of  subjects  most 
similar  to  the  freshman  subject  is  usually  the  best  criterion.  As  was  sug- 
gested in  Chapter  III,  however,  accuracy  of  prediction  can  usually,  if 
not  always,  be  increased  by  using  multiple  rather  than  simple  correla- 
tion, or,  in  other  words,  by  basing  prediction  upon  two  or  more  of  the 
items  of  information  rather  than  upon  a  single  one.  How  much  doing  so 
increases  accuracy  of  prediction  will  be  shown  in  the  next  chapter. 

Summary  and  comparison  of  the  results  secured  in  this  study 
with  those  in  the  studies  of  others.  On  the  whole  the  degrees  of  rela- 
tionship of  freshman  marks  with  age,  test  score  and  high-school  marks 
found  in  this  study  are  not  very  different  from  those  obtained  by  other 
investigators.  Those  with  age  are  so  small  as  to  be  negligible  for  pur- 
poses of  prediction.  The  correlation  between  freshman  average  and  test 
score,  .38,  is  slightly,  but  not  a  great  deal,  lower  than  the  central  ten- 
dency of  a  large  number  of  studies.  Undoubtedly  this  is  accounted  for 
by  two  facts  referred  to  in  discussing  the  reliability  of  the  results  in 
Chapter  III.    These  are  that  the  test  used  is  considerably  shorter  than 


[^'-^ 


most  tests  employed  for  the  same  purpose  and  therefore  does  not  yield 
as  reliable  measures  and  that  marks  from  a  great  many  institutions 
were  grouped  together,  thus  introducing  more  variations  in  standards 
than  would  be  found  in  the  marks  of  a  single  institution.  The  correla- 
tions between  freshman  and  high-school  subjects  found  by  the  writer 
tend  to  run  about  the  same  as  those  obtained  in  the  two  studies  of  this 
sort  to  which  reference  is  made. 

Combining  the  evidence  from  all  the  studies  along  this  line  with 
which  the  writer  is  familiar  the  statement  seems  warranted  that  in  gen- 
eral a  score  on  any  one  of  the  best  intelligence  tests  and  the  proper  high- 
school  mark  have  about  equal  value  in  predicting  probable  freshman 
marks.  In  each  case  the  general  expectation  concerning  the  size  of  the 
coefficient  of  correlation  is  that  it  will  be  somewhere  between  .40  and 
.50,  though  under  the  best  conditions  one  can  reasonably  expect  to  se- 
cure at  least  some  simple  correlations  of  .60  or  higher. 


[33] 


CHAPTER  V 

THE  MULTIPLE  CORRELATIONS  BETWEEN  FRESHMAN 
MARKS  AND  THE  OTHER  DATA  COLLECTED 

The  multiple  coefficients  of  correlation  computed.  Although  a 
brief  statement  as  to  what  multiple  correlations  were  found  was  made 
in  Chapter  III  it  seems  best  to  repeat  it  here  in  somewhat  more  com- 
plete form.  Seventeen  subjects  from  among  the  49  carried  by  ten  or 
more  freshmen  each  were  selected  for  this  procedure.  All  but  one  or 
two  of  these  were  the  subjects  carried  by  the  largest  numbers  of  fresh- 
men, these  one  or  two  being  added  because  of  some  especial  interest  in 
them.  In  three  of  the  subjects,  chemistry,  French,  and  Latin,  two  sets 
of  multiple  correlations  were  computed,  one  for  all,  or  almost  all,  fresh- 
men carrying  the  subject  and  another  only  for  those  who  had  also  car- 
ried certain  high-school  subjects.  In  Spanish,  three  sets  of  coefficients 
were  found,  two  special  groupings  being  made  according  to  the  high- 
school  subjects  carried.  Thus,  including  the  general  freshman  average. 
23  sets  of  multiple  coefficients  were  computed. 

The  procedure  in  computing  the  multiple  coefficients  was  first  to 
select  all  of  the  simple  coefficients  of  correlation  which  seemed  worth 
using,  the  number  so  selected  varying  from  two  to  six,  and  then  to 
combine  these  to  secure  the  multiple  ones.  The  two  always  used  were 
the  general  high-school  average  and  the  point  score.  In  addition  to  these 
the  high-school  average  in  the  group  of  subjects  and  the  mark  in  the 
one  or  more  single  subjects  most  similar  to  the  college  freshman  sub- 
ject were  also  included,  except  in  two  or  three  cases  in  which  no  high- 
school  subjects  that  could  be  said  to  be  similar  had  been  carried  by 
enough  pupils  to  be  worth  including.  The  one  marked  example  of  this 
was  ph}-sical  education,  almost  none  of  the  freshmen  who  carried  this 
subject  having  marks  recorded  for  any  similar  work  in  high  school.  In 
a  few  cases  age  was  used.  In  a  number  of  instances  the  computations 
were  begun  with  more  criteria  than  were  carried  through  to  the  finish, 
since,  as  the  work  progressed  it  could  be  seen  that  some  of  those  used 
made  no  contributions.  In  each  case  the  work  with  those  included  was 
carried  to  the  point  that  no  further  increase  as  great  as  .01  was  ob- 
tained by  computing  multiple  coefficients  of  higher  orders.  In  the  ma- 
jority of  cases  the  number  of  criteria  required  to  accomplish  this  end 
was  three,  in  three  cases  four  were  required  and  in  none  more;  in  one 
case  the  highest  zero  order  coefficient  could  not  be  increased  and  in  the 

[34]  i 


remaining  ones  two  were  all  that  was  necessary.  In  this  connection  the 
reader  should  again  be  reminded  that  many  of  the  criteria  used,  such  as 
the  general  high-school  average,  the  high-school  science  average,  the 
high-school  mathematics  average,  and  the  high-school  foreign  language 
average,  were  themselves  combinations  of  marks  in  several  different 
subjects  and  therefore  the  simple  correlations  with  them  were  in  a  sense 
multiple,  although  not  computed  by  multiple  methods.  Because  of  this 
fact  the  increases  above  the  simple  coefficienets  were  not  nearly  as  great 
as  if  no  such  averages  had  been  used. 

The  multiple  coefRcients  of  correlation  obtained  in  this  study. 
The  highest  multiple  coefficients  obtained  in  this  study  along  with 
related  data  are  presented  in  Table  IV.  The  first  set  of  four  columns 
therein  is  for  the  highest  simple  coefficient  of  correlation  obtained  for 
each  of  the  subjects  mentioned,  the  second  group  of  four  for  the  highest 
multiple  coefficient  and  the  last  group  of  three  for  the  increase  of  the 
multiple  over  the  simple  coefficient.  Within  each  of  the  two  groups  of 
four  the  first  column,  headed  "r"  and  "R,"  contains  the  actual  coeffi- 
cients of  correlation,  the  second,  headed  "k,"  the  corresponding  coeffi- 
cients of  alienation,  the  third,  headed  "P.E.  ,"  the  corresponding  prob- 
able errors  of  estimate  and  the  fourth  the  one  or  more  criteria^  used 
in  the  correlations.  The  last  three  columns  contain,  in  order,  the  in- 
creases in  the  highest  multiple  over  the  highest  simple  coefficients  of  cor- 
relation and  the  accompanying  decreases  in  the  coefficients  of  aliena- 
tion and  the  probable  errors  of  estimate.-  For  example,  taking  the  first 
line  of  the  table,  the  highest  simple  coefficient  of  correlation  of  freshman 
algebra  mark  with  any  single  criterion  was  .52,  the  corresponding  co- 
efficient of  alienation  was  .85,  the  probable  error  of  estimate  6.4  and  the 
criterion,  high-school  mathematics  average.  The  highest  multiple  corre- 
lation obtained  for  algebra  was  .53,  with  a  coefficient  of  alienation  of 
.85  and  a  probable  error  of  estimate  of  6.4.  It  was  based  on  two  criteria, 
high-school  mathematics  average  and  high-school  general  average.  The 
increase  in  the  coefficient  of  correlation  was  .01,  whereas  there  was  no 
change  in  the  coefficient  of  alienation  or  the  probable  error  of  estimate. 

^It  will  be  noted  that  in  a  few  cases  in  the  table  the  abbreviations  for  two  of  the 
criteria  are  connected  by  the  word  '"or."  This  means  that  in  such  cases  the  correlation 
based  on  the  two  was  the  same  or  so  nearly  the  same  that  it  makes  no  appreciable  dif- 
ference which  one  is  used.  For  example,  in  the  case  of  geometry,  the  simple  correla- 
tions with  high-school  geometry  mark  and  high-school  mathematics  mark  differed  by 
only  .0004,  so  that  it  makes  no  material  difference  which  one  is  used. 

^It  should  be  remembered  that  an  increase  in  the  coefficient  of  correlation  and  de- 
creases in  the  coefficient  of  alienation  and  the  probable  error  of  estimate  indicate  closer 
relationship  or  greater  accuracy  of  prediction. 

[  ro  ] 


z 

w 

w 

^ 

X 

ZH 

o 

o 

•— 1 

z 

'f 

1— t 

H-1 

H 

w 

u 

a: 
o 
u 

Q 

a; 

O 

z 

Z 

Q 

UJ 

D 

u 

< 

b; 

Ul 

w 

O 

H 

u 

DS 

w 

u 

J 

r/^ 

CL, 

D 
O 

D 

< 
> 

Q  Q 

z  z 

< 

< 

W 

en 

t^ 

a, 

cc 

S 

< 

c/2 

s 

H  Z 

O) 

<r' 

UJ 

I 

O 
X 

X 

ta 

> 

1— ' 

w 

hJ 

n 

< 

H 

^ 

£ 

1 

«    (L)    c 

U 

c 

"" 

^~ 

r 

— 

O 

Q^ 

o 

r-^        ~        ri       •— 

^ 

c 

c 

c      o      c      c 

O 

B3     t)     OJ 

S  cx-a 

t:5  E 

Lh 

_ 

t 

't 

<: 

i>n 

fN 

fn        —        Tf        r- 

«N 

C    3-^ 

c 

^  E 

cii 

" 

"rt 

"5  or 

u 

cr 

■y: 

6  ,'u: 

or. 

.    re     .     , 

c/: 

'C 

C 

< 

^a. 

Cl. 

<      -■  CCL 

U 

J=  ^ 

E~ 

^ 

"  uT 

-  J" 

"  J   r  E  ::    r-  J 

^     • 

-S-^  rt 

3> 

u 

-    rcA 

<u  t; 

!L1  V 

iltCU&CUC/jCUtC.  ijut; 

<U    i) 

D.  <-'.- 

-^'u 

:^a. 

>  — 

> 

>  c 

>  c 

>     .  u  >  c   o  >  ■- 

>    bJC 

X  ^  S3 

U-y: 

<X<a. 

<'J. 

<'hI- 

<cxo<ute<3:<<| 

2  c-c 
£  o  u 

^ 

j_,    ■*-'  ^^ 

c) 

^ 

vy- 

(^ 

r 

^^ 

r^ 

c- 

C^         ro        oc        f^ 

o 

Highes 
correla 
severa 

vC 

VC 

^ 

W" 

-t 

Tt- 

w- 

»-r,         r^         ur,          Lr 

■* 

lO 

>-n 

r^ 

^H 

c 

(N 

iJ-.         -1-         r-         O 

^ 

^ 

00 

oc 

oc 

oc 

OC 

oc           O.          OC           OC 

o 

f^ 

r- 

_^ 

r 

r-- 

ro       "^        O        ^ 

■* 

Pi 

•^ 

u-i 

-*■ 

-* 

-i- 

vC 

1^1 

U-.        r-2        lo        ■* 

CO 

c 

o 

L- 

ij 

c 

■w 

mple 

with 

terion 

£ 

0. 

8. 
> 

1. 
> 

> 

0. 

> 

51 
> 

E-^ 

c  -       ^ 

t        a. 
> 

> 

u 

J- 

< 

< 

< 

< 

<;j^     UJ     < 

< 

■".25 

1 

't 

vC 

r- 

C 

o 

w- 

't 

C        r-i        o-        -t 

Ov 

ghes 
relat 
one 

a-* 

^ 

■vC 

^C 

t 

"t 

^ 

SC              I-~              "-.              LT 

^ 

K  8  « 

'-'    rt 

u- 

r~ 

C^ 

f-N 

r- 

Tl 

•^ 

r~       Tf       c>       C 

w-1 

^ 

oc 

oc 

oc 

o- 

O 

oc 

oc 

oc        o.        oc        o^ 

C> 

rJ 

a- 

m: 

o- 

m: 

u- 

yj- 

C             Tf             ■VO             f 

fN 

tH 

t 

Tf 

f 

c 

ly- 

w 

•y^             to             '*'             "t 

CO 

C 

*-•                  * 

1) 

5             ^ 

_c 

X 

0. 

t      J 

c 
:       c 
'        c 

t. 

t. 

c 

0. 

2     ^      «      ^ 
=      11^ 

a;         oj         4,       .- 

"•         C 

.a 

to 

< 

:    L. 

)       L 

)     u 

fcL 

i      tt 

U 

C 

C 

C 

I 

El 

136} 


trt   (U   c 

i;j=  o 

en    l>   oj 

&■£  S 


o  o 


_.    OJ    1) 


_C   aj  o 


U 


-H        ro        O        r-4        —        <N         CN        -^O        ^^ 


*^  *50  ,       C       y,       rt 

-•3    ^  — ^  t: 


W^IJh;^ 


;  f^  uT 


c/i  c/}  J  c/o 

Oh'  cC    o  oI 


CLiQh 


rJ  J 


<ta 


>  .  .>  .>>cc>co>oo^>> 


oi 


(1) 

cfl 

4-* 

tuO 

s 

(U 

^ 

JO 

0 

3 

O  CO 


w 


>  c  > 


to 


>  o 


^  CO 
LO  to 


^  CO 


«    r:    w 


•n     •;:      x 


c  c 


II  a-  *"■" 


-a  3 


M 


j=.t: 


-IS  o 


2  ^  S  = 


^  -  .  —  „  •  -  c 


-T3    u•- 


=  -^  3  C  o'c 


3      .-  uHHjsj;  — 

°  "  c^  S  «  %  «  i 
t;        _  3  i.   -     1- 

u  rt  ;,  3  c  ><  "  — x: 

^^    °    11    u)  S   Mi-<   2 

j=-5  "_3  lij  S-c  ,3  S 

■-J=    U--   ^__c  j^ 

«  "^     „  o-fi  I-  S  " 

=  S  3  .j'^^-s^.s. 
«  3=i£'ti'o  « 

«"«.-.  ^^-a  *--  ^  o 
-a       =  n^  °l^-=  f 

M       ^.       t;       2      ^J=.li-C_^ 

.:;  6  =1  ^  g  3-c^ 

1  J=        'i~ 


"s-'o  P,  c 


=  £  -  - 

c  b:  r'  n 


'  ^  e- 


*^  n  »*   _ 


U   O-  u   CO   c   3   S       _»; 
C    M    Q    J*    «•-—    3    U 

_ii  o  u  u  JJ  >.•■"  d_ 


[37] 


The  increases  of  multiple  over  simple  indices  of  relationship.    A 

comparison  of  the  multiple  with  the  simple  coefficients  shows  that  on  the 
whole  there  was  little  increase  in  the  latter.  In  one  case  out  of  the  23 
the  highest  simple  coefficient  could  not  be  raised  by  including  other  cri- 
teria. The  median  increase  produced  was  only  .03  and  the  greatest  .07, 
with  corresponding  decreases  in  the  coefficient  of  alienation  ranging 
from  zero  to  .05,  over  three-fourths  of  them  being  .02  or  smaller.  As  re- 
gards the  probable  error  of  estimate  over  half  of  the  cases  were  de- 
creased by  .1  and  in  only  one  case  was  the  difference  more  than  .2.  In 
other  words,  the  increased  reliability  of  prediction  obtained  in  this  study 
by  using  the  best  multiple  correlations  and  regressions  is  so  small  that 
it  is  very  doubtful  if  it  can  be  said  to  be  worth  the  additional  labor  and 
expense  required. 

The  criteria  of  highest  predictive  value.  In  addition  to  the  fact 
just  mentioned  probably  the  one  of  chief  interest  in  the  table  is  the 
question  of  what  criteria  are  most  valuable  as  bases  for  predicting  fresh- 
man marks.  It  was  shown  in  the  preceding  chapter  that  in  many  cases 
the  high-school  average  yielded  the  highest  correlation  with  the  fresh- 
man mark,  whereas  in  many  others  some  similar  subject  or  group  of 
subjects  did  so.  Of  the  25^  criteria  employed  in  the  simple  correlations 
given  in  this  table,  the  high-school  average  appears  in  13  cases,  the  aver- 
age mark  in  a  similar  group  of  high-school  subjects  in  six,  that  in  a  sim- 
ilar high-school  subject  in  five,  and  the  point  score  only  a  single  time, 
for  physical  education.  The  criteria  used  in  obtaining  the  multiple  co- 
efficients run  very  similarly  except  that  the  point  score  appears  a  much 
larger  number  of  times.  In  approximately  three-fourths  of  the  cases  the 
high-school  average  Is  one  of  the  criteria  and  the  same  is  true  of  the 
point  score.  Single  subject  marks  occur  somewhat  less  frequently  and 
those  in  groups  of  subjects  in  less  than  half  of  the  cases.  It  appears  that 
although  the  simple  correlations  between  the  point  score  and  freshman 
marks  are  in  general  decidedly  lower  than  those  of  the  latter  with  the 
high-school  average  and  with  marks  in  various  subjects  and  groups  of 
subjects,  yet  the  point  score  makes  a  contribution  in  prediction  some- 
what distinct  from  that  made  by  the  other  criteria  mentioned. 

Summary  of  this  chapter.  Multiple  coefficients  of  correlation  were 
computed  for  about  one-third  of  the  freshman  subjects,  in  a  few  cases 
more  than  one  set  being  computed  for  each  subject.  These  coefficients 
run  from  .20  up  to  .63,  most  of  them  being  between  .40  and  .60,  al- 


ibis number  includes  the  two  criteria  giving  practically  equal  coefficients  in  ge- 
ometry and  rhetoric. 


[38] 


though  five  are  at  or  above  the  latter  figure.  The  accompanying  co- 
efficients of  alienation  range  from  .98  down  to  .78,  most  of  them  being 
In  the  eighties  and  the  probable  errors  of  estimate  from  7.3  down  to 
about  half  that  amount.  For  the  general  freshman  average  the  multiple 
coefficient  is  .58,  the  coefficient  of  alienation  .81  and  the  probable  error 
of  estimate  3.7.  In  no  case  were  more  than  four  criteria  needed  to  se- 
cure the  highest  coefficient  and  In  most  cases  only  two  or  three.  The 
increases  In  the  multiple  above  the  simple  coefficients  and  the  decreases 
In  the  corresponding  coefficients  of  alienation  and  probable  errors  of 
estimate  are  so  small  that  the  very  slightly  Increased  reliability  of  pre- 
diction appears  not  to  be  worth  the  additional  labor  of  computing.  With 
two  or  three  bare  exceptions  the  estimates  possible  are  still  four-fifths  or 
more  pure  guesses  and  In  the  case  of  about  one-fourth  of  the  subjects 
they  are  nine-tenths  or  more  pure  guesses. 


[39] 


CHAPTER  VI 

THE  ACCURACY  OF  PREDICTIONS  BASED  UPON  THE 
OBTAINED  COEFFICIENTS  OF  CORRELATIONS 

Purpose  of  this  chapter.  To  anyone  who  has  not  had  considerable 
experience  in  deaHng  with  predictions  when  the  degree  of  relationship 
is  expressed  by  coefficients  of  correlation  the  mere  statement  that  a  co- 
efficient of  correlation  is  so  much,  .35  or  .60  for  example,  generally  has 
little  definite  meaning,  especially  as  indicating  how  accurate  the  predic- 
tions are.  In  the  two  chapters  dealing  with  the  correlations  found  in 
this  study  a  few  brief  references  have  been  made  to  their  interpretation 
in  other  terms,  but  it  seemed  best  to  devote  a  chapter  to  a  more  elabor- 
ate treatment  of  the  matter.  The  attempt  will  be  made  to  show  in  two 
or  three  ways  just  how  many  and  how  great  are  the  errors  present  in 
predictions  associated  with  coefficients  of  correlation  of  sizes  typical  of 
those  obtained  in  this  and  other  similar  investigations.  The  writer  has 
discussed  the  matter  at  somewhat  greater  length  elsewhere^  and  will  not 
attempt  to  reproduce  in  full  what  has  been  said  there,  but  will  repeat  a 
portion  of  it  with  some  additional  suggestions  concerning  Interpretation. 

Interpretation  of  the  coefficient  of  correlation,  in  terms  of  the  co- 
efficient of  alienation  or  of  a  "pure  guess."  In  connection  with  the 
coefficients  of  correlation  presented  in  Chapters  IV  and  V  some  figures 
were  given  and  statements  made  as  to  what  they  meant  in  terms  of  pure 
guesses.  For  example,  in  one  place  it  was  stated  that  a  coefficient  of  .52 
indicated  that  predictions  based  thereon  were  only  15  per  cent  better 
than  pure  guesses.  To  understand  this  and  similar  statements  one  needs 
to  know  what  is  meant  by  a  pure  guess.  It  assumes  that  the  person 
making  the  prediction  or  guess  knows  what  the  distribution  of  the  meas- 
ures which  are  being  predicted  is,  but  does  not  have  any  information  at 
all  which  helps  him  to  determine  which  measure  belongs  to  any  partic- 
ular case.  For  example,  if  one  were  making  a  pure  guess  concerning 
the  marks  to  be  assigned  the  members  of  a  high-school  freshman  alge- 
bra class  from  their  previous  records  it  would  be  assumed  that  he  knew 
the  distribution  of  marks  which  would  be  given,  but  that  he  had  no  in- 
formation at  all  as  to  which  mark  would  be  given  to  each  individual 
pupil. 

'Odell,  C.  W.  '"The  Interpretation  of  the  probable  error  and  the  coefficient  of 
correlation."  University- of  Illinois  Bulletin,  Vol.  23,  No.  52,  Bureau  of  Educational  Re- 
search Bulletin  No.  32.    Urbana:  University  of  Illinois,  1926,  p.  28-32  and  39-45. 

[40] 


The  conception  of  a  pure  guess  can  probably  be  made  more  mean- 
ingful by  employing  a  concrete  example.  For  this  purpose,  let  us  sup- 
pose that  in  a  high-school  freshman  algebra  class  the  teacher  has  decided 
that  the  marks  she  will  issue  will  consist  of  two  A's,  seven  B's,  twelve 
C's,  five  D's  and  four  E's.  Let  us  suppose  further  that  someone  is  told 
that  this  distribution  of  marks  is  to  be  given  and  that,  without  knowing 
anything  about  the  Individual  pupils  which  in  any  way  concerns  their 
scholastic  ability  or  achievement,  he  attempts  to  predict  the  marks  each 
one  will  receive.  He  will,  of  course,  select  two  individuals  as  those  who 
will  receive  A's,  seven  as  those  who  will  receive  B's,  twelve  C's  and  so 
on.  Since  his  selections  or  predictions  are  not  based  upon  any  knowledge 
whatsoever  which  helps  him  in  determining  the  marks  assigned  individ- 
ual students,  they  will  be  subject  to  the  same  errors  as  if  any  purely 
chance  method  was  used,  such  as  placing  the  names  of  the  pupils  in  a 
hat  and  predicting  that  the  first  two  drawn  would  receive  A's,  the  next 
seven  B's,  and  so  on.  In  either  case  the  predictions  made  are  pure  guesses 
and  the  relationship  between  them  and  the  actual  marks  is  represented 
by  a  coefiicient  of  correlation  of  zero.- 

For  predictions  to  be  a  certain  per  cent  better  than  pure  guesses 
means  that  on  the  average  the  errors  involved  in  such  predictions  are 
smaller  than  those  involved  in  pure  guesses  by  the  given  per  cent.  To 
illustrate  this,  let  us  suppose  that  if  pure  guesses  are  made  in  a  certain 
situation  they  involve  one  error  of  15  points,  one  of  14,  two  of  13,  two 
of  12,  and  so  on.  With  predictions  40  per  cent  better  than  pure  guesses 
the  errors  would  be  40  per  cent  smaller,  so  that  it  might  be  expected 
that  instead  of  the  error  of  15  points  there  would  be  one  of  9  points,  in- 
stead of  the  one  of  14  points  there  would  be  one  of  8.4  points,  likewise 
two  of  7.8  points,  two  of  7.2  points,  and  so  on.  Sometimes  the  size  of 
the  errors  is  expressed  in  just  the  opposite  way  to  that  so  far  used  in 
this  paragraph,  that  is  to  say,  instead  of  saying  that  predictions  are  40 
per  cent  better  than  pure  guesses  one  may  say  that  they  are  60  per  cent 
pure  guesses  or  that  the  errors  involved  are  60  per  cent  as  large  as  those 
in  pure  guesses. 

Table  V  shows  how  the  predictions  based  on  coefficients  of  correla- 
tion of  given  sizes  compare  with  pure  guesses.  In  this  table,  the  first 
column  contains  values  of  the  coefficient  of  correlation  at  intervals  of 
.01  from  1.00  down  to  .95  and  at  intervals  of  .10  from  .90  down  to  .00, 
with  the  coefiicient  of  alienation  or  fraction  of  a  pure  guess  correspond- 

^In  actual  practice  a  coefficient  of  exactly  zero  will  rarely  be  obtained  because 
with  a  small  number  of  cases  the  element  of  chance  agreement  or  disagreement  between 
prediction  and  actual  facts  is  fairly  large. 

[41] 


TABLE  V.     COEFFICIENTS  OF  ALIENATION*  CORRESPONDING  TO 
CERTAIN  VALUES  OF  THE  COEFFICIENT  OF  CORRELATION 


I 


Coefficient 

Coefficient          1 

Coefficient          1 

Coefficient 

of 

of 

of 

of 

Correlation 

Alienation 

Correlation 

Alienation 

1.00 

.0000 

.70 

.7141 

0.99 

.1411 

.60 

.8000 

0.98 

.1990 

.50 

.8660 

0.97 

.2431 

.40 

.9165 

0.96 

.2800 

.30 

.9539 

0.95      - 

.3122 

.20 

.9798 

0.90 

.4359 

.10 

.9950 

0.80 

.6000 

1                 .00 

1.0000 

*The  coefficient  of  alienation  is  obtained  by  solvingv  1  — r^,  in  which  r  is  the  symbol  for  the  co- 
efficient of  correlation. 


ing  to  each.  Beginning  at  the  top  of  the  table  It  will  be  seen  that  when 
the  correlation  is  perfect  and  the  coefficient  1.00,  the  coefficient  of  aliena- 
tion is  zero,  or,  in  other  words,  prediction  can  be  made  with  absolute 
accuracy.  When  the  correlation  is  .99,  the  prediction  is  about  .14  of  a 
pure  guess,  when  it  is  .98  the  prediction  is  .20  of  a  pure  guess,  and  so 
on.  One  can  see  that  the  inaccuracy  of  prediction  or  the  fraction  of  a 
pure  guess  involved  therein  incfeases  very  rapidly  at  first  for  compara- 
tively small  decreases  in  the  coefficient  of  correlation.  By  the  time  the 
latter  reaches  .80,  the  errors  in  predictions  are  .'60  as  large  as  those  in 
pure  guesses,  and  when  the  correlation  is  .50  the  errors  are  almost  .87 
as  large  as  those  in  pure  guesses. 

If  one  now  recalls  the  sizes  of  the  coefficients  of  correlation  between 
freshman  marks  and  other  criteria,  and  then  the  corresponding  coeffi- 
cients of  alienation,  he  will  see  at  once  how  unreliable  are  the  best  pre- 
dictions of  college  marks  which  can  be  made  upon  the  basis  of  these 
criteria.  IMost  of  the  obtained  simple  coefficients  of  correlation  were  be- 
low .50,  very  few  rising  above  this.  Thus  for  most  of  them  the  best 
predictions  possible  are  87  per  cent  or  more  pure  guesses.  A  very  few 
of  the  simple  coefficients,  and  not  a  great  many  of  the  multiple  ones, 
rose  above  .60.  For  one  of  .60  the  errors  in  prediction  are  .80  as  large 
as  those  in  pure  guesses  and  for  one  of  .65,  not  given  In  the  table,  they 
are  .76  as  large.  The  general  statement  may  therefore  be  made  that, 
with  one  or  two  possible  exceptions,  the  best  predictions  possible  from 
the  criteria  used  In  this  study  are  still  subject  to  errors  which  are  on 
the  whole  three-fourths  as  large  as  those  in  pure  guesses  and  that  in 
most  cases  they  are  at  least  four-fifths  or  five-sixths  as  large.  In  other 
words,  they  are  so  large  that  probably  the  most  that  can  be  said  for 
predictions  based  upon  these  or  similar  criteria  Is  that  if  it  Is  necessary 


[42] 


or  highly  advisable  to  make  selection  or  classification  of  some  sort, 
these  criteria  furnish  a  somewhat  better  basis  for  doing  so  than  would 
mere  guesses. 

Interpretation  of  the  coefficient  of  correlation  in  terms  of  the 
probable  error  of  estimate.  Another  means  of  describing  the  accuracy 
of  prediction  based  on  a  coefficient  of  correlation  of  a  given  size  is  to 
state  the  probable  error  of  estimate.^  The  probable  error  of  estimate  is 
easily  obtained  after  the  coefficient  of  alienation  has  been  found  as  all 
that  is  necessary  is  to  multiply  the  latter  by  the  median  deviation*  of 
the  distribution  in  question.  The  meaning  of  the  probable  error  of  esti- 
mate is,  in  a  general  way,  the  same  as  that  of  any  other  probable  error 
or  median  deviation,  that  is,  half  of  the  errors  involved  in  making  esti- 
mates or  predictions  are  less  than  the  probable  error  and  half  are 
greater,  about  82  per  cent  are  less  than  twice  the  probable  error  and 
18  per  cent  greater,  almost  96  per  cent  less  than  three  times  the  prob- 
able error  and  slightly  over  4  per  cent  greater,  and  so  on.  For  example, 
a  probable  error  of  four  points  in  connection  with  estimates  of  fresh- 
man marks  in  algebra  would  mean  that  half  of  the  estimates  or  predic- 
tions of  the  marks  made  by  individual  students  would  be  in  error  by 
less  than  four  points  and  half  by  more,  that  about  82  per  cent  of  them 
would  be  an  error  by  less  than  eight  points  and  about  18  per  cent  by 
more,  and  so  on.  The  form  of  statement  may  be  changed  to  read  that 
the  chances  are  even  that  the  error  in  the  case  of  any  particular  indi- 
vidual is  not  greater  than  four  points,  that  they  are  about  4.6  to  1  that 
it  is  not  greater  than  twice  this  amount  or  eight  points,  22  to  1  that  it  is 
not  greater  than  three  times  the  probable  error  or  twelve  points,  and 
so  on.^ 

It  will  be  recalled  that  the  probable  errors  of  estimate  given  in 
Chapter  V  as  corresponding  to  the  highest  multiple  coefficients  of  corre- 
lation obtained  were  mostly  between  four  and  six  points,  though  one  or 
two  were  slightly  smaller  than  four  points  and  several  larger  than  six, 
one  even  being  above  seven.  The  central  tendency  was  somewhat  above 
five.    In  other  words,  on  the  average,  predictions  of  college  freshman 


'The  standard  error  of  estimate  might  also  be  used,  but  the  discussion  will  be 
confined  to  the  probable  error  because  it  is  probably  more  generally  understood  and 
used.   The  standard  error  is  1.4826  times  the  probable  error. 

"Since  the  median  deviation  equals  .6745  times  the  standard  de\iation,  the  usual 

formula  for  the  probable  error  of  estimate  is  .6745<r  V  1 — r^,  in  which  cr  is  the  abbre- 
viation for  the  standard  deviation. 

In  case  the  standard  error  has  been  used  instead  of  the  probable  error  the  inter- 
pretation along  the  lines  given  above  must,  of  course,  be  appropriately  changed.  The 
proper  per  cents  and  chances  for  this  purpose  may  be  found  in  Odell,  op.  cit.,  p.  14. 

[43] 


TABLE  VI.     APPROXIMATE  DISTRIBUTIONS  OF  COLLEGE  FRESHMAN 
MARKS  AS  COMPARED  WITH  PREDICTIONS  THEREOF  COR- 
RESPONDING TO  VALUES  OF  THE  COEFFICIENT  OF 
CORRELATION  OF  .40,  .50,  .60  and  .70 


r  =  .40 

r  =  .50 

Criterion 

Freshman  Mark 

Criterion 
Rating 

Freshman  Mark 

Rating 

E 

D 

C 

B 

A 

T   ' 

E 

D 

C 

B 

A 

T 

A 

1 

3 

3 

3 

10 

A 

3 

3 

4 

10 

B 

1 

9 

8 

6 

3 

20 

B 

4 

7 

6 

3 

20 

C 

3  • 

8 

18 

8 

3 

40 

C 

3 

7 

20 

7 

3 

40 

D 

3 

6 

8 

2 

1 

20 

D 

3 

6 

7 

4 

20 

E 

3 

3 

3 

1 

10 

E 

4 

3 

3 

10 

T 

10 

20 

40 

20 

10 

100 

T 

10 

20 

40 

20 

10 

100 

r=.60 

r  =  .70 

Criterion 

Freshman  Mark 

Criterion 
Rating 

Freshman  Mark 

Rating 

E 

D 

C 

B 

A 

T 

E 

D 

C 

B 

A 

T 

A 

2 

3 

5 

10 

A 

1 

3 

6 

10 

B 

3 

7 

7 

3 

20 

B 

2 

7 

8 

3 

20 

C 

2 

/ 

22 

7 

2 

40 

C 

1 

7 

24 

7 

1 

40 

D 

3 

7 

7 

3 

20 

D 

3 

8 

7 

2 

20 

E 

5 

3 

2 

10 

E 

6 

3 

1 

10 

T 

10 

20      40 

20 

10 

100 

T 

10 

20 

40      20 

10 

100 

marks  in  particular  subjects  based  upon  the  combination  of  criteria 
which  gave  the  best  prediction  in  each  case  would  contain  errors  of 
more  than  five  points  in  about  half  of  the  cases,  of  almost  eleven  points 
in  about  18  per  cent,  and  of  about  sixteen  points  in  over  4  per  cent. 
The  predictions  of  the  general  freshman  average,  which  had  the  small- 
est probable  error  of  estimate,  would  be  in  error  by  almost  four  points 
or  more  in  half  of  the  cases,  by  about  seven  and  one-half  or  more  in  18 
per  cent  of  the  cases,  and  by  over  eleven  points  in  4  per  cent  of  the 
cases.  In  view  of  the  fact  that  the  total  range  of  passing  marks  is  only 
30.  it  can  be  seen  how  serious  errors  of  this  size  are  and  how  little  reli- 
ability such  predictions  possess.  On  the  average  about  one-half  of  the 
students  who  would  really  receive  freshman  marks  of  75  would  be  rated 
below  70  or  as  failing,  about  18  per  cent  of  those  who  made  80  would 
be  rated  as  failing  and  about  4  per  cent  of  those  making  85  would  be 
so  rated.  Similar  per  cents  would  of  course  be  rated  too  high  as  well  as 
too  low.  It  is.  therefore,  evident  that  a  great  amount  of  individual  in- 
justice would  be  done. 

Interpretation  of  the  coefficient  of  correlation  in  terms  of  the 
frequency  and  amount  of  displacement.    Another  method  of  making 


[44] 


TABLE  VII.     SUMiMARY  OF  THE  AMOUNT  OF  AGREEMENT  AND  DIS- 
AGREEMENT BETWEEN  PREDICTIONS  AND  ACTUAL  FRESH- 
MAN MARKS  SHOWN  IN  TABLE  VI 


Number  of  Divisions  Displaced 

r 

0 

1 

2 

3 

4 

T 

.70 

52 

40 

8 

0 

0 

56 

.60 

46 

40 

14 

0 

0 

68 

.50 

40 

40 

20 

0 

0 

80 

.40 

36 

44 

16 

4 

0 

88 

more  concrete  the  meaning  of  predictions  based  upon  coefficients  of  cor- 
relation is  to  compute  the  numbers  of  individual  cases  which  would  not 
be  correctly  predicted  if  classified  in  a  few  groups  on  the  basis  of  prob- 
able academic  success.  Since  what  is  probably  the  most  common  system 
of  marking  in  college  makes  use  of  five  letters  and  since  many  high 
schools  likewise  do  the  same,  the  interpretations  to  be  given  will  be 
based  upon  this  number  of  divisions.  That  is  to  say,  it  is  assumed  that 
high-school  marks  and  other  criteria  employed  are  represented  by  only 
five  marks  and  college  success  likewise  by  five.  It  is  further  assumed 
that  the  distribution  of  marks  in  each  case  is  such  that  10  per  cent  each 
of  the  highest  and  lowest  marks  are  given,  20  per  cent  each  of  the  next 
to  the  highest  and  next  to  the  lowest  and  40  per  cent  of  average  marks. 
For  purposes  of  convenience  these  marks  are  called  A,  B,  C,  D,  and  E, 
A  being  the  highest  and  E  the  lowest.  The  interpretations  given  are  for 
coefficients  of  correlation  of  .40,  ,50,  .60  and  .70,  as  this  range  includes 
practically  all  of  the  highest  ones  obtained  in  this  study.  The  most 
likely  symmetrical  distribution  in  each  case  is  shown  in  Table  VI.  The 
upper  left-hand  quarter  of  the  table,  for  a  coefficient  of  .40,  shows  that 
of  ten  individuals  for  whom  the  criterion  rating  or  prediction  was  A, 
only  three  would  on  the  average  actually  receive  A's,  three  B's,  three 
C's,  and  one  D.  For  the  twenty  for  whom  B's  were  predicted  three 
would  get  A's,  six  B's,  eight  C's,  two  D's  and  one  E,  and  so  on.  Look- 
ing through  all  four  tables  it  is  readily  seen  that  as  the  correlation  in- 
creases the  number  of  exact  agreements  between  prediction  and  fact  be- 
comes closer.  Thus  when  r  =  .50,  four  of  the  ten  whose  predicted 
standing  is  A  actually  receive  that  mark,  for  r  =  .60,  five  actually  re- 
ceive it,  and  for  r  =  .70,  six. 

Although  such  tables  as  those  above  give  a  rather  concrete  idea  of 
the  situation,  yet  because  of  the  fact  that  each  contains  many  entries  It 
is  rather  hard  to  get  a  general  or  summary  idea  thereof.  This  is  perhaps 


[45] 


better   accomplished   by   taking  one   more   step    and   tabulating,   as    in 
Table  \TI  above,  the  numbers  of  cases  out  of  the  hundred  in  which  thai 
agreement  is  perfect,  the  number  in  which  there  is  one  step  disagree-J 
ment,  two  steps  disagreement  and  so  on.    The  bottom  line  of  the  tabU 
for  r  ^  .40  corresponds  to  the  upper  left-hand  fourth  of  Table  \T.    It 
shows,  first,  that  36  of  the  hundred  cases  agree  exactly.   This  number  isl 
obtained  by  adding  the  three  cases  which  it  is  predicted  will  and  which] 
do  receive  A's,  the  six  which  are  predicted  to  and  do  receive  B's,  thej 
eighteen  similar  C's,  the  six  D's  and  the  three  E's.  or  in  other  words  byJ 
adding  the  five  entries  lying  on  a  diagonal  line  from  the  upper  right-^ 
hand  to  the  lower  left-hand  corner.  Furthermore,  44  of  the  one  hundredl 
cases  show  an  error  or  displacement  of  one  division  between  predictions' 
and  actual  marks.   This  is  obtained  by  taking  the  sum  of  the  two  diag- 
onal rows  next  to  the  one  from  corner  to  corner,  one  being  on  each  side 
of  it.    Continuing,  there  are  16  cases  which  are  displaced  two  divisions 
or  letters  and  4  which  are  displaced  three.    The  total  amount  of  dis- 
placement, given  in  the  last  column.  Is  88  and  is  found  by  multiplying 
each  of  the  entries  in  that  row  by  the  amount  of  displacement  under 
which  it  falls  and  adding  the  products.  Thus  44X1  +  16X2+4X3=88. 
It  will  be  seen  that  even  if  r  ^  .70,  which  is  a  much  higher  correlation 
than  was  obtained  in  the  case  of  practically  any  of  the  freshman  sub- 
jects dealt  with  in  this  study,  only  slightly  over  half  of  the  cases  are 
correctly  predicted  and  that  the  total  displacement  amounts  to  a  shift 
of  56.  The  figures  for  r  =  .50  and  .60  more  nearly  portray  the  situation 
existing  in  most  subjects  and  show  that  in  less  than  half  of  the  cases 
would  accurate  predictions  be  made,  that  in  about  two-fifths  of  them 
predictions  would  be  in  error  by  one  division  or  letter,  and  in  one-fifth 
or  less  by  two. 

Summary  of  this  chapter.  Since  statements  of  the  closeness  of 
relationship  between  freshman  marks  and  various  other  items  of  infor- 
mation do  not  Indicate  very  concretely  the  size  of  the  errors  involved  in 
predicting  the  former  from  the  latter  when  made  in  terms  of  coefficients 
of  correlation,  several  other  means  have  been  used.  These  are  the  co- 
efficient of  alienation,  the  probable  error  of  estimate,  and  a  statement  of 
the  frequency  and  amount  of  displacement.  It  appears  that  with  one  or 
two  rather  doubtful  exceptions  the  best  predictions  possible  from  the. 
available  criteria  have  coefficients  of  alienation  of  three-fourths  oi 
larger,  or.  In  other  words,  the  errors  present  are  at  least  three-fourths 
as  large  as  they  would  be  If  pure  guesses  were  made.  The  corresponding 
probable  error  of  estimate  Is  not  far  from  five  points,  which  means  thai 


[46] 


half  of  the  predictions  would  be  in  error  by  more  than  this  amount. 
Computing  the  displacement  on  the  assumption  of  five  divisions  In  both 
criteria  and  freshman  marks  the  best  predictions  would  result  in  the  dis- 
placement of  about  half  of  the  individuals  by  one  or  two  divisions.  Thus 
on  the  whole  it  is  apparent  that  the  errors  present  in  the  best  predictions 
are  both  numerous  and  large  and  that  if  the  predictions  are  used  com- 
paratively little  confidence  should  be  placed  in  them. 


[47] 


CHAPTER  VII 

IS  THE  CHANGE  FROM  HIGH  SCHOOL  TO  COLLEGE 

GREATER  THAN  THAT  FROM  ELEMENTARY 

TO  HIGH  SCHOOL? 

A  further  statement  of  the  question.    A  problem  which  has  not 
Infrequently  been  discussed,  especially  since  the  public  high  school  has 
become  such  an  important  part  of  our  educational  system,  is  that  ofj 
the  breaks  between  the  elementary  and  the  high  school  and  between  thai 
high  school  and  the  college.    It  has  frequently  been  claimed  and  the 
claim  fairly  well  supported  that  too  great  a  break  occurs  at  one  or  both] 
places  and  that  those  in  school  are  subjected  to  too  abrupt  a  transition. 
It  occurred  to  the  writer,  therefore,  that  it  might  be  a  matter  of  interesti 
to  present  very  briefly  a  few  comparative  data  which  would  tend  to 
show  which,  if  either,  of  the  two  changes  was  the  greater. 

The  data  to  be  used  in  the  comparison.  One  means  of  determining 
how  great  the  change  is  from  one  type  of  school  to  another  is  by  means 
of  the  correlation  between  marks  before  and  after  the  transition.  Thus 
the  correlations  obtained  between  high-school  and  college  freshman 
marks  in  this  study  are  in  a  sense  measures  of  the  similarity  of  work 
done  by  the  same  individuals  in  high  school  and  college  and  of  the  con- 
ditions under  which  this  work  is  done.  Likewise  correlations  between 
elementary-school  and  high-school  marks  may  be  considered  as  similar 
measures  in  that  case.  Although  such  correlations  are  in  neither  case 
perfect  or  entirely  satisfactory  measures  yet  they  are  in  both  cases  sub- 
ject to  practically  the  same  limitations  and  therefore  may  be  fairly  com- 
pared with  each  other. 

Instead  of  making  an  exhaustive,  or  even  fairly  wide,  study  and 
compilation  of  the  various  correlations  obtained  between  elementary  and 
high-school  marks,  the  writer  has  selected  a  single  study^  along  this  line 
and  will  compare  the  results  given  in  it  with  those  obtained  in  his  own 
study.  This  study  was  selected  because  it  appears  to  be  one  of  the  most 
carefully  conducted  investigations  dealing  with  this  problem  which  has 
been  carried  out  and  also  includes  data  for  a  number  of  groups  of  pupils. 


^Ross,  C.  C.  "The  relation  between  grade  school  record  and  high  school  achieve- 
ment." Teachers  College  Contributions  to  Education,  No.  166.  New  York:  Teachers, 
College,  Columbia  University,  1925.   70  p.  *• 


[48] 


TABLE  VIII.     COEFFICIENTS  OF  CORRELATION  BETWEEN  MARKS  IN 
ELEMENTARY  AND  HIGH-SCHOOL  FRESHMAN  SUBJECTS* 


Elementary 
.  School 
Subject 

High-School  Freshman 

Subject 

Average 

English 

Mathematics 

Arithmetic 

.52 
.59 
.35 
.50 
.40 
.35 
.36 
.26 

.44 
.50 
.48 
.50 
.40 
.46 
.45 
.43 

.38 

English 

Fine  Arts 

.34 
.08 

Geography 

.28 

History 

.24 

Reading 

.18 

Spelling.  .  . 
Special  Sub. 

.18 
.03 

'Taken  from  Ross,  op.  cit.,  p.  15. 


TABLE  IX.     COEFFICIENTS  OF   CORRELATION   BETWEEN   ELEMEN- 
TARY-SCHOOL  AVERAGE  AND  HIGH-SCHOOL  FRESHMAN  MARKS* 


High-School  Freshman  Subject 

Average 

English 

Latin 

Mathematics 

New  Rochelle,  1916. 
New  Rochelle,  1917. 
New  Rochelle,  1918. 
New  Rochelle,  1919. 
Des  Moines 

.68 
.67 
.56 
.65 
.69 

.60 
.67 
.67 
.60 
.61 

.58 
.73 
.57 
.64 
.61 

.42 
.51 
.43 
.51 
.51 

*Taken  from  Ross,  op.  cit.,  p.  35. 


Tables  \  III  and  IX  present  some  of  the  correlations  which  Ross 
obtained.  In  the  first  will  be  found  those  between  marks  in  eight  ele- 
mentary-school subjects  or  groups  of  subjects  and  the  high-school  fresh- 
man average,  English  mark  and  mathematics  mark.  The  second  gives 
those  between  elementary-school  average  and  high-school  freshman  av- 
erage, English,  Latin,  and  mathematics  marks.  It  will  be  seen  that  the 
coefficients  given  in  Table  VIII  run  from  very  near  zero  up  to  slightly 
above  .50,  those  of  the  elementary-school  subject  marks  with  mathe- 
matics being  decidedly  lower  than  those  with  freshman  average  and 
English  marks,  which  on  the  whole  do  not  differ  greatly.  The  central 
tendency  of  the  latter,  that  is,  of  the  correlations  with  both  freshman  aver- 
age and  English  mark  is  somewhat  above  .40,  whereas  that  for  mathe- 
matics mark  is  not  far  from  .20.  In  the  case  of  the  elementary-school 
averages  given  in  Table  IX  the  correlations  are  distinctly  higher  and 
also  more  uniform.  For  the  freshman  average  and  English  and  Latin 
marks  they  are  practically  all  in  the  sixties,  but  in  mathematics  again 
somewhat  lower. 


[49] 


Comparison  of  the  results  of  Ross  and  of  the  writer.  When  these 
are  compared  with  the  coefficients  given  in  Table  III  and  discussed  in 
Chapter  I\'  at  least  two  facts  are  evident.  Those  in  Table  VHI  on  the 
whole  run  very  much  the  same  as  do  the  corresponding  ones  in  Table 
III.  The  correlations  of  the  several  elementary  subject  marks  with  the 
freshman  average  tend  to  be  about  the  same  as  those  of  the  particular 
college  freshman  subject  marks  with  the  high-school  average  and  like- 
wise those  of  the  elementary  ones  with  English  and  mathematics  marks 
fall  in  about  the  same  range  as  those  of  the  particular  high-school  and 
college  freshman  subject  marks.  The  fact  that  several  of  those  for  math- 
ematics in  Table  VTII  are  lower  than  any  corresponding  ones  in  Table 
III  is  undoubtedly  due  to  the  fact  that  the  correlations  between  subject 
marks  found  in  the  writer's  study  and  given  in  Table  III  are  only  those 
which  it  seemed  likely  would  be  fairly  high,  whereas  no  such  selection 
was  employed  in  finding  those  in  Table  VIII.  The  second  noticeable 
fact  is  that  the  coefficients  in  Table  IX  tend  to  be  decidedly  higher  than 
the  corresponding  ones  in  Table  III.  The  correlation  between  high- 
school  average  and  college  freshman  average  was  only  .55,  whereas  the 
lowest  one  between  elementary-school  and  high-school  freshman  average 
is  .56  and  their  average  .65,  .10  greater  than  that  between  high-school 
and  college.  Those  between  the  high-school  average  and  the  college 
freshman  marks  in  particular  subjects  were  only  in  two  or  three  cases  as 
high  as  .60  and  more  often  below  .50  than  above,  whereas  eight  out  of 
the  15  given  in  Table  IX  are  .60  or  above  and  only  two  below  .50;  On 
the  whole  the  difference  in  this  case  is  probably  best  represented  by  at 
least  .15  rather  than  .10. 

Conclusion.  The  evidence  just  presented  supports  the  conclusion  i 
that  the  break  between  elementary  school  and  high  school  is  not  as 
marked  as  that  between  high  school  and  college.  Inasmuch  as  it  is  prob- 
ably true  that  there  are  greater  differences  in  the  subject  matter  of  ele- 
mentary-school and  high-school  subjects  than  in  that  of  high-school  and 
college  subjects,  the  higher  correlations  in  the  former  case  imply  that 
other  factors  therein  must  both  balance  this  greater  difference  in  subject 
matter,  and  also  indicate  greater  similarity  otherwise.  The  chief  factor  is 
probably  that  elementary  and  high  schools  are  usually  united  and  under 
the  same  general  control  within  particular  school  systems,  and  that  both 
their  aims  and  methods  of  instruction  tend  to  be  more  similar  than  is 
true  in  the  case  of  high  schools  and  colleges.  In  most  high  schools  pu- 
pils are  subjected  to  fairly  close  supervision  and  their  work  consists 
largely  in  performing  very  definitely  specified  assignments  under  more 

[50] 


or  less  guidance  from  teachers,  whereas  In  college  very  little  control  is 
usually  exercised  over  their  study  habits  and  assignments  are  often 
much  more  indefinite.  In  other  words,  it  seems  that  in  high  school  as 
well  as  in  elementary  school  the  prevailing  practice  is  to  treat  the  pu- 
pils as  relatively  irresponsible  children,  whereas  in  college  they  are  ex- 
pected to  assume  full  individual  responsibility. 


[31] 


CHAPTER  VIII 
SUMMARY  AND  CONCLUSIONS 

The  problem.  The  very  marked  recent  Increase  in  college  enroll- 
ment has  had  as  one  of  its  results  a  considerable  growth  of  interest  in 
the  problem  of  selecting  from  applicants  for  admission  to  college  those 
who  will  be  able  to  do  satisfactory  work  therein,  and  therefore  in  meth- 
ods of  predicting  scholastic  success  in  college.  Most  of  the  investigations 
along  this  line  have  dealt  with  making  such  predictions  on  the  basis  of 
high-school  marks,  college  entrance  examinations  over  high-school  sub- 
jects, and  intelligence  test  scores. 

Results  secured  by  other  investigators.    The  results  obtained  by 
a  rather  large  number  of  investigators  may  be  summarized  by  saying] 
that  there  is  probably  little  difference  in  the  accuracy  of  predictions 
based  upon  these  three  different  criteria  and  that  most  of  the  coeffi-j 
cients  of  correlation  between  any  one  of  them  and  college  marks  may! 
be  expected  to  range  from  about  .40  to  .50  or  perhaps  higher;  that  com- 
binations of  these  factors  will  often  yield  correlations  of  .60  or  above; 
and  that  if  measures  of  study  and  other  relevant  habits  are  included  this] 
figure  can  be  raised  appreciably. 

The  writer's  results.  A  study  conducted  by  the  writer  which  in- 
cluded almost  two  thousand  college  freshmen  in  over  a  hundred  dif- 
ferent institutions  did  not  deal  with  ordinary  entrance  examinations  or 
with  study  habits.  The  correlations  found  between  high-school  and 
freshman  marks  were  about  the  same  as  those  obtained  by  other  inves- 
tigators and  those  between  test  scores  and  freshman  marks  somewhat 
lower,  undoubtedly  due  to  the  fact  that  the  test  used  was  not  the  most 
reliable  one  available  for  this  purpose.  When  multiple  correlation  was 
employed  comparatively  small  increases  were  produced  in  the  coeffi- 
cients, only  a  few  of  them  rising  above  .60  when  the  best  combinations 
of  school  marks  and  test  scores  were  made.  This  was  largely  due  to  the 
fact  that  many  of  the  high-school  marks  used  in  simple  correlation  were 
averages  of  several  subjects.  In  this  connection  it  should  be  noted  that 
the  correlations  obtained  in  the  writer's  study  were  undoubtedly  low- 
ered somewhat  because  of  the  throwing  together  of  school  marks  from 
hundreds  of  different  high  schools  and  colleges  which  must  have  intro- 
duced errors  that  lowered  the  coefficients. 


[52] 


Accuracy  of  predictions  based  on  obtained  data.  Coefficients  of 
correlation  of  the  sizes  usually  found,  that  is  from  .40  up  to  .50  or  even 
.60,  indicate  that  the  corresponding  predictions  of  freshman  marks  are 
not  a  great  deal  better  than  pure  guesses.  Predictions  corresponding  to 
the  highest  of  these  coefficients  are  still  subject  to  errors  at  least  three- 
fourths  as  large  as  those  in  pure  guesses  or,  in  terms  of  points  on  the 
percentile  marking  scale,  at  least  half  of  the  errors  in  the  estimates  are 
larger  than  five  points.  It  should,  however,  be  pointed  out  that  high 
scores  upon  intelligence  tests  and  also,  but  probably  to  a  lesser  degree, 
high  high-school  or  entrance  examination  marks  are  more  reliable  than 
low  ones  and  more  confidence  may  be  placed  in  them  as  indicating  pos- 
sibilities of  student  performance.  Comparatively  few  individuals  earn 
scores  or  marks  much  above  what  they  really  deserve,  but  many  fairly 
able  individuals,  through  indifference,  carelessness,  temporary  distrac- 
tion or  other  causes,  make  scores  or  marks  too  low  to  be  indicative  of 
the  abilities  which  they  possess.  One  is  reasonably  safe,  therefore,  in 
assuming  that  an  individual  who  is  rated  high  by  all,  or  even  by  any 
one,  of  the  three  criteria — intelligence  test,  high-school  mark,  and  col- 
lege entrance  examinations — is  able  to  do  reasonably  satisfactory  or 
better  work  in  college,  whereas  the  fact  that  an  individuars  score  is  low 
in  one  of  them  or  perhaps  even  in  all  is  not  nearly  so  sure  an  indication 
that  he  cannot,  if  he  will,  do  satisfactory  work,  although  the  chances  are 
strong  that  if  his  scores  are  low  in  all  three,  his  scholastic  work  in  col- 
lege will  also  be  decidedly  poor. 

Comparative  break  between  elementary  and  high  school  and  be- 
tween high  school  and  college.  A  comparison  of  the  results  of  this 
study  with  those  obtained  by  Ross  in  predicting  high-school  from  ele- 
mentary-school marks  shows  that  the  correlations  in  the  latter  case  are 
distinctly  higher,  the  diflterences  averaging  .10  or  .15.  In  other  words, 
it  appears  that  the  similarity  of  the  work  done  or,  more  likely,  of  the 
conditions  prevailing,  in  elementary  and  high  school  is  greater  than  it  is 
in  the  case  of  high  school  and  college. 

Conclusion  as  to  the  use  of  the  available  criteria  for  predicting 
I?  scholastic  success  in  college.  Since  both  for  the  purpose  of  determin- 
ing the  admission  of  applicants  to  college  and  of  personnel  work  with 
students  who  have  been  admitted,  it  is  desirable  to  predict  the  quality 
of  their  scholastic  work,  it  is  better  to  make  use  of  such  bases  of  pre- 
diction as  we  have  than  to  rely  upon  pure  guesses.  Therefore  the  use  of 
high-school  marks,  entrance  examination  results,  or  intelligence  test 
scores  for  this  purpose  is  better  than  that  of  no  criterion   at  all.    It 

[53]  ■ 


should  be  recognized,  however,  that  the  errors  present  are  decidedly 
large  and  that  the  predictions  of  the  work  to  be  done  by  individuals 
cannot  be  relied  upon  as  possessing  a  high  degree  of  accuracy.  The 
writer  wishes  to  emphasize  as  strongly  as  possible  the  need  for  further 
experimentation  and  investigation,  especially  along  the  line  of  determ- 
ining which  criteria  form  the  best  combinations  for  predictions  based 
upon  multiple  correlation  and  regression  equations.  He  believes  that  a 
combination  of  the  score  upon  one  of  our  best  intelligence  tests  for  this 
purpose,  such  as  that  of  Thorndike,  of  the  marks  in  certain  high-school 
subjects  or  groups  of  subjects  and  on  the  best  types  of  entrance  exami- 
nations over  these  subjects,  of  the  ratings  of  study  habits  and  perhaps 
other  factors,  can  be  combined  so  that  practically  any  institution  can  ob- 
tain correlations  of  .75  or  .80  between  the  marks  of  Its  students  and  the 
best  available  combination. 


[54] 


